For convenience sake, I've gathered up all of the information from Cox into one long(!) post as follows:
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I want to present some information from John Harrington Cox's collection of West Virginia folk songs, including a number of the "Child Ballads". I want to again thank Richie for calling my attention to this collection. This is a good source for demonstrating how source singers "remember" the origins of their songs. Here is a link to Cox's book, published in 1925, although most of the ballads seem to come from a decade or so earlier:

http://archive.org/stream/folksongsofsouth00coxj#page/n7/mode/2up

Here is an example of a biographical sketch of one of the ballad singers represented in Cox, named George W. Cunningham of Elkins, West Virginia.

http://archive.org/stream/folksongsofsouth00coxj#page/n23/mode/2up

Cox had four ballads from him. Mr. Cunningham's memory sources don't go back as far as some of the others. For instance, he says he learned his version of Child Ballad #4, "Six Kings' Daughters", "shortly after the Civil War from Laban White, Dry Fork." Here is the link for that:

http://archive.org/stream/folksongsofsouth00coxj#page/6/mode/2up

One of the source singers in Cox's collection is Mrs. Rachel Fogg, who was originally from Doddridge County, WVA. There were four Child Ballads obtained from her by Mrs. Hilary G. Richardson, in Clarksburgy, Harrison County, WVA, in March of 1916. They were: "Down by the Greenwood Side", "Little Johnnie Green" (Barbara Allen), "Young Collins"/"Johnny Collins", and "The House Carpenter".

In each case, Mrs. Fogg said that she had learned the ballad from her mother, and she from her mother. In one instance, she added "on back into the old country across the sea", and in another instance, she added "...on back into the old country across the sea in Scotch, Dutch, or Jerusalem, she forgets which but in this country they call'em Hebrews."

Here are the links:

http://archive.org/stream/folksongsofsouth00coxj#page/28/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/108/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/110/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/146/mode/2up

Here is an account of Cox's visit with Mrs. Fogg:

http://archive.org/stream/folksongsofsouth00coxj#page/n27/mode/2up

And here is a picture of Mrs. Fogg:

http://archive.org/stream/folksongsofsouth00coxj#page/112/mode/2up

Here is some more information from J.H. Cox's collection. He has four ballads from Mrs. Elizabeth Tapp Beck, of Morgantown in Monongalia County, which were collected in March of 1916. There is "Lord Thomas and Fair Eleanor," "The House Carpenter," "Home Came The Old Man (#274)," and "The Golden Willow Tree." Cox says that she said that she learned these songs from her mother, Mrs. Thomas H. Tapp, who learned it from her mother, Mrs. Elizabeth Wade Mack, who lived "near Bethel Church" near Easton. Here are the links:

http://archive.org/stream/folksongsofsouth00coxj#page/64/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/148/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/154/mode/2up

http://archive.org/stream/folksongsofsouth00coxj#page/170/mode/2up

Continuing with some more information from John Harrington Cox's West Virginia collection in "Folk Songs of the South", here are several sources which seem to go back a ways.

Cox has "The King's Daughter" or "The False Lover" from Miss Mildred Joy Barker, of Morgantown in Monongalia County, WVA, on October 2, 1916, which was "obtained from her mother, whose family came to Monongalia County before the Revolution. Its members have known the ballad for years."    Here is the link:

http://archive.org/stream/folksongsofsouth00coxj#page/12/mode/2up

Cox has another version of this ballad (#4) called "Pretty Polly" sent to him by Mrs. Anna Copley, of Shoals in Wayne County, WVA, on December 19, 1915, "dictated by her cousin Mr. Burwell Luther, who learned it from his mother about fifty years ago. Mrs. Luther's name was Julia Stephenson. She learned it from her mother, whose maiden name was Peyton. The Peytons were English and the Stephensons were Highland Scotch. The Luthers and Stephensons have lived in Wayne County for over a century, the latter having come from Georgia." Here is the link:

http://archive.org/stream/folksongsofsouth00coxj#page/8/mode/2up

Then there is a version of "Lord Randall" called "Johnny Randolph," which was "Communicated by Miss Lily Hagans, Morgantown, Monongalia County, January 20, 1916; obtained from Mrs. Beulah Ray Richey, who learned it from her mother, a member of the Caldwell family of Wheeling, a family of Irish [Scots-Irish?] descent who came to Wheeling before the Revolution." Here is the link:

http://archive.org/stream/folksongsofsouth00coxj#page/26/mode/2up

Here are two versions of "Lord Lovel", one from a lady of English descent and one from a lady of Welsh descent. The first one, "Lord Lovel," was "Contributed by Miss Blanche Satterfield, Fairmont, Marion County, 1915; learned from her mother, who learned it from her mother, a lady of English descent, who came from Washington County, Pennsylvania."

http://archive.org/stream/folksongsofsouth00coxj#page/78/mode/2up

The second version of "Lord Lovel" was "Communicated by Miss Lucille V. Hays, Glenville, Gilmer County, November 22, 1916; obtained from her mother, who learned it from her mother, and she from her mother, Mrs. Zackwell Morgan, a lady of Welsh descent."

http://archive.org/stream/folksongsofsouth00coxj#page/82/mode/2up

Continuing with some more material from John Harrington Cox, here are three ballads collected from Mr. J. Harrison Miller, of Wardensville in Hardy County, WVA, in January and june of 1916. First there is "The Seven Sleepers" (#7), which Mr. Harrison "obtained from his mother, who learned it when a girl from Scotch Roach."

http://archive.org/stream/folksongsofsouth00coxj#page/18/mode/2up

Then there is "Johnny Randolph" (#12), which was "obtained from his mother; learned from Susan Stewart; she, from her stepfather, John Jennings, who came from England."

http://archive.org/stream/folksongsofsouth00coxj#page/24/mode/2up

And then there is the version of "Lord Thomas", which Richie called our attention to above. This ballad was "obtained from his mother, who learned it from her mother, Mrs. Lucinda Ellis, who learned it from her grandmother, Mrs. Strawnsnider. Mr. Miller thinks the ballad has been known in the family for about two hundred years."

http://archive.org/stream/folksongsofsouth00coxj#page/56/mode/2up

Here are two ballads from Mrs. J.J. Haines of Parkersburg in Wood County, WVA, collected in January of 1916. There is a version of "Fair Annie and Gregory" (#76). Mrs. Haines said, "I have heard these old ballads sung form my earliest recollection by my grandparents and others. Grandfather's name was Benjamin Franklin Roberts; grandmother's name was Mary Leatherman Roberts. Grandfather's mother was a descendant of the Franklins, but I do not know whether of Benjamin Franklin's father's family, or a brother. My ancesters on both sides came to America in the time of the colonization."

http://archive.org/stream/folksongsofsouth00coxj#page/82/mode/2up

And from the same sources, Mrs. Haines had a version of "The House Carpenter" :

http://archive.org/stream/folksongsofsouth00coxj#page/148/mode/2up

Here are five versions of "The Wife of Usher's Well" that have some interesting "remembered" lineages. The first one is called "A Moravian Song", and illustrates something of the history of the relationships between the Scots-Irish and the German immigrants in WVa. It was contributed by Miss Bettie R. Loy, of Glebe, in Hampshire County, WVA, in February of 1916. Miss Loy writes: "I am sending you a song that my mother learned of her mother, who was of Dutch descent, but either she or her parents learned it of a Moravian preacher and she called it a Moravian song."

http://archive.org/stream/folksongsofsouth00coxj#page/88/mode/2up

The second version was called "Lady Gay", and was contributed by John B. Adkins of Branchland, in Lincoln County, WVA, in February, 1916. He learned it "when a child from an aunt, who learned it from her mother."

http://archive.org/stream/folksongsofsouth00coxj#page/90/mode/2up

The third example of this ballad was communicated by Mr. Decker Toney, of Queen's Ridge, in Wayne Count, WVA, in January of 1916. It was "learned from his mother, who learned it from her mother, Hannah Moore, and she, from her mother, Hannah Ross, who was born in Virginia." Back when Hannah Ross was born, West Virginia was still a part of Virginia, so it is not clear what this reference might mean. But it seems to imply what was once known as "East Virginia" or the eastern part of Virginia. See the previous link for this version which is "D".

The fourth and fifth versions were collected by the same person. They were communicated by Miss Mary M. Atkeson, of Morgantown in Monongalia county, WVA, in December of 1915. The first one ("E") was "obtained from Mr. Joseph H. Spicer, Spring Gap, in Hampshire County, WVA; learned from his mother, who learned it from her grandmother, who came from Ireland."

The last version ("G") was "obtained from Mr. A.G. Springer, Farmington, Marion County; dictated by his mother, who learned it from her mother, a lady of Welsh and English ancestry, who came from Pennsylvania."

http://archive.org/stream/folksongsofsouth00coxj#page/92/mode/2up

In 1916, Cox had two ballads collected by Miss Lalah Lovett, of Bulltown in Braxton County, WVA. The first one was a version of "Barbara Ellen", "obtained from Mrs. Cora Starkey, Harrison County, who learned it when a child from her parents; they learned it in Virginia from their parents, who were of English descent."

http://archive.org/stream/folksongsofsouth00coxj#page/100/mode/2up

The second ballad collected by Miss Lovett, was a version ("J") of "The House Carpenter", which was also obtained from Mrs. Cora Starkey.

http://archive.org/stream/folksongsofsouth00coxj#page/148/mode/2up

Here are a few more Child Ballads from John Harrington Cox's collection from WVA. The first one is a version of "The Maid Freed from the Gallows" called "By a Lover Saved". It was communicated to Cox by Mr. Harold Staats, of Ripley, in Jackson County, WVA, in 1921, Mr. Staats wrote: "This song was told, or rather sung, to me by some person living on Tug Fork. It is claimed that this song was brought to this country by Captain William Parsons, one of the early settlers. According to legends it was at one time a popular folk song in the British Isles."
An interesting account. Parsons was one of the first settlers who came over the Alleghenies to settle in what is now Tucker County, WVA.

http://archive.org/stream/folksongsofsouth00coxj#page/118/mode/2up

Then we have a version of Child #155 called "It Rained a Mist", which was "Communicated by Miss Violet Hiett, Great Cacapon, Morgan County, February, 1917; obtained from her father, who learned it when a child from his mother."

http://archive.org/stream/folksongsofsouth00coxj#page/120/mode/2up

Another version of Child #155 ("I") came from Mr. Richard Elkins Hyde, of Martinsburg, in Berkeley County, WVA, in December of 1916. It was "obtained from his mother, who learned it from her mother, who had it from her mother, a lady of good Scotch-Irish stock from Wardensville, Hardy County."

http://archive.org/stream/folksongsofsouth00coxj#page/126/mode/2up

Here are two rarer ballads that Cox found in West Virginia. The first one is Child #199, "The Bonnie House O' Airlie" and the second one is Child #201, "Bessie Bell and Mary Gray." The first one was "Contributed by Miss Fannie Eagan, Hinton, Summers County, January 12, 1917, learned from Miss Amelia Bruce, who was born and bred in Edinburgh, came to America about twenty years previously, and recently returned to Scotland to remain there." This example is of interest not because it documents an early date necessarily, but because it documents an example of the actual transmission of a ballad from Scotland to America.

http://archive.org/stream/folksongsofsouth00coxj#page/128/mode/2up

The second ballad was "Communicated by Miss Eva Hughes, Spencer, Roane County, December 7, 1915; obtained from her mother, whose maiden name was Elmira Grisell, born near Malaga, Ohio, in 1837. She learned it from her mother, who was Elizabeth Adams, daughter of Ann Hazlett and Jonathan Adams (English) of Massachusetts. Elizabeth's parents died when she was a child, and she was brought up by her aunt, Betsy Adams, Horne, Darby, Pennsylvania."

http://archive.org/stream/folksongsofsouth00coxj#page/134/mode/2up

There are two more examples of Child #243, "The House Carpenter". One was "communicated by Mr. Greenland Thompson Federer, Morgantown, Monongalia County, January 1917; taken from an old manuscript song book owned by Lizzie Kelly, Independence. A name at the end of the ballad seems to indicate that it was taken down from the dictation of Mary Guseman."

http://archive.org/stream/folksongsofsouth00coxj#page/140/mode/2up

The second example called "Salt Water Sea" ("Q") was "communicated by Miss Sallie Evans, Randolph County, 1916; obtained from Mr. Guy Marshall, who got it from his mother, who learned it from her mother."

http://archive.org/stream/folksongsofsouth00coxj#page/148/mode/2up

There is version of "The Suffolk Miracle" (Child #272) called "A Lady near New York Town." It was contributed by Miss Polly McKinney, of Sophia in Raleigh County, WVA, in 1919. Miss McKinney wrote: "Grandma Lester taught me the song when I was a little child. Grandma is eighty-five years old. She says the song is very old. Her mother taught it to her when she was a little girl."

http://archive.org/stream/folksongsofsouth00coxj#page/152/mode/2up

Mr. Wallie Barnett of Leon, in Mason County, WVA, contributed a version of Child #277, called "Dandoo." He learned it from his grandfather "about the year 1898" His grandfather "was of English descent, a native of Gilmer County. The last stanza was furnished by some teacher whose name was not secured." (Cox)

http://archive.org/stream/folksongsofsouth00coxj#page/158/mode/2up

And finally, my last example from Cox is a version of Child #275, "Get Up And Bar The Door", called "Old John Jones." Cox says: "this excellent text, agreeing well with Child B, was reported by Mr. Carey Woofter, Glenville, Gilmer County, September, 1924. It was taken down from the recitation of Mrs. Sarah Clevenger of Briar Lick Run, near Perkins, Gilmer County. She learned it from her grandmother, Mrs. Rebecca Clevenger, who came from Loudon County, Virginia, seventy-eight years ago, as the date in the family Bible gives it."

http://archive.org/stream/folksongsofsouth00coxj#page/516/mode/2up