I'm not saying the melody is exactly the same but the contour is (which is the quick recognition I use) and the form (text) is the same. The Irish melody I know and sing is the same as the Quinn covers Richard Thompson, Tim Hart and Maddy Prior, Oysterband, Fleet Foxes, and Outside Track to name a few. To me it was instantly clear that the Coates and Quinn are the same after looking at the Coates melody.
It's clear to me, and you may disagree, but the Coates, Jane Hicks Gentry/ Maude Gentry are the same type as Quninn's type. We don't know if Mrs. Coates nee Allen learned it from her family or her husband's so its conjecture- just hat the Coates family was in Cheraw SC in the late 1700s and moved to NC from there.
This is what I have for the Irish versions- which is quite different than Edmunds:
A. Irish versions; including versions from America from Irish/American informants (standard melody: "Uist Tramping Song" c. 1700s ref. Ulster Folklife) a. False Knight- my title, two stanzas sung by a madwoman in the Dublin area from the novel: "Women, Or, Pour Et Contre: A Tale," page 26 by Charles Robert Maturin, 1818. b. "False Knight On The Road." Sung by Margaret Sullivan (Mrs. E.M. Sullivan) about 1865. From Flanders Ancient Ballads, 1966 and Ballads Migrant in New England, 1932. Sullivan was born in County Cork, Ireland about 1855. Learned in her childhood. c. "Fol Fly on the Road." Sung before 1870, in Fort Kent, Me., by a French girl who could speak very little English, as learned from an illiterate Irish family. From "The False Knight upon the Road," A, Folk-Songs of the North Atlantic States recollected by M. L. F., Portland, Me., Oct. 16, 1907. Also published in The Journal of American Folklore, Vol. 24, No. 93 (Jul. - Sep., 1911), pp. 344-349. d. "Knight on the Road" Sung by Mrs. T. G. Coates of Flag Pond, Tennessee on Sept. 1, 1916. From Sharp MSS 3369/2466; Sharp & Karpeles, English Folksongs from the Southern Appalachians, 1932, I p. 3. e. "Knight in the Road." Sung by Mrs. Jane (Hicks) Gentry, from Madison County, NC, was one of Cecil Sharp's main informants. Sharp & Karpeles, English Folksongs from the Southern Appalachians, 1932, I p. 4. f. "The Smart Schoolboy." Sung by Preston Wolford of Virginia, 1935, collected by John Jacob Niles; from Niles, Ballad Book, 1966. g. "The False Knight upon the Road" Sung by Mrs. Maud Long of Hot Springs, North Carolina, at Washington, D. C., 1947. Recorded by Duncan Emrich. h. "The False Knight on the Road" sung by Frank Quinn of Coalisland, Co. Tyrone, Ireland in 1958 as recorded by Sean O'Boyle. Topic, The Folksongs of Britain IV, 'The Child Ballads'. Also in J. Taylor & Michael Yates, eds., Ballads and Songs, Vol 6.
Edmunds includes several versions which are not similar enough to include in the group. Some of the versions in this group are not the same form.
There's also an Irish/Newfoundland group (False false Fly) which has text from Child 1 which includes Barry Gleeson/Ben Henneberry (NL) Archie Fisher etc. Barry's version (c. 1870) may be part of that group only one stanza.
Brian thanks for pointing out the similarity between Creighton & Senior) and Dearnley. There's not a tradition in England but these should be separate.
Hard to categorize these- I can't agree with Edmunds who doesn't consider the melody- she doesn't give the Coates as related melodically and instead give Niles version which seems to be based on Coates. Edmunds includes a number of versions under the "Irish" group which I can't include.