Bob Waltz (above) wrote the Traditional Ballad Index entry for Mary Mack. It might be helpful if I posted the entire thing:

Mary Mack (I)

DESCRIPTION: "Oh Mary Mack, Mack, Mack, All dressed in black, black, black...." The singer speaks of love, and engages in a series of unprofitable transactions. Much of the song consists of floating verses, e.g. "I went to the river... And I couldn't get across."
AUTHOR: unknown
EARLIEST DATE: 1846 (Halliwell)
KEYWORDS: playparty nonballad courting commerce | black buttons clapping
FOUND IN: Britain(England(West)) US(MA,MW,NW,SE,SW,So) Australia Canada(Newf) Ireland
REFERENCES (22 citations):
Courlander-NegroFolkMusic, pp. 158-159, "(Mary Mack)" (1 text); p. 279, "Mary Mack" (1 tune, partial text)
Lomax/Lomax-OurSingingCountry, pp. 72-73, "Johnnie Bought a Ham" (1 text, 1 tune)
Opie/Opie-TheSingingGame 145, "Miss Mary Mack" (4 texts, 1 tune)
Solomon-ZickaryZan, pp. 24-25, "(Mary Mack)" (notes, filed under "Pease Porridge Hot"); p. 58, "Mary Mack" (1 text)
Byington/Goldstein-TwoPennyBallads, p. 110, "Mary Mack" (1 text)
Cray-AshGrove, pp. 14-15, "Mary Mack" (1 text, 1 tune)
Gundry-CanowKernow-SongsDancesFromCornwall, p. 44, "(Harvey-Darvy dressed in black)" (1 fragment with this form although it's short enough it might be something else, 1 tune, filed with a group of songs under the general heading "Crowdy Crawn")
Brady-AllInAllIn, p. 66, "(Mary Mac, Mac, Mac)" (1 text)
JournalOfAmericanFolklore, Winifred Smith, "A Modern Child's Game Rhymes," Vol. IXL, No. 151 (Jan 1926), #6 p. 83, ("Mary Mack, dressed in black"); #9 p. 83 ("Tinkle bells and cockle shells, E-V-I-V over, Mary Mack, dressed in black") (2 texts)
JournalOfAmericanFolklore, Leah Rachel Clara Yoffie, "Three Generations of Children's Singing Games in St. Louis," Vol. LX, No. 235 (Jan 1947), p. 41 ("Mary Mack, Mack, Mack") (1 text)
Averill-CampSongsFolkSongs, p. 499, "Oh Mary Mack Mack Mack" (notes only)
Abrahams-JumpRopeRhymes, #120, "Mary Mack, dressed in black" (1 text)
ADDITIONAL: Miss Allen, "Children's Game-Rhymes" in Relics of Popular Antiquities, &c , The Folk-Lore Record (London, 1878 ("Digitized by Google")), Vol. V, #14 p. 87, "Darby's Son" (1 text)
Henry Carrington Bolton, Counting-Out Rhymes of Children (New York, 1888 ("Digitized by Google")), #795 p. 117, ("Miss Mary Mack, dressed in black") (1 text)
James Orchard Halliwell, The Book of Nursery Rhymes Complete (Philadelphia, 1846 ("Digitized by Google")), #413 p. 202, ("Parson Darby wore a black gown"); #421 p. 205, ("Darby and Joan were dress'd in black") (2 texts)
G.F. Northall, English Folk-Rhymes (London, 1892 ("Digitized by Google")), p. 395, ("Betsy Blue came all in black, Silver buttons down her back"), ("Darby's son was dressed in black, With silver buttons behind his back"); p. 387 ("Darby and Joan were dress'd in black, Sword and buckle behind their back"), ("Parson Darby wore a black gown, And every button cost half-a-crown") (4 texts)
Mrs Lois Rather, "Circle Clap Chants" in Western Folklore, Vol. XVIII, No. 4 (Oct 1959 (available online by JSTOR)), #2 p. 294 ("Say, Say, Say, O Mary Mac, Mac, Mac") (1 text)
Anna Raudnitzky, "The Greatest Thing in the School-Room" in N.C. Schaeffer, editor, The Pennsylvania School Journal, Vol. XLVII (Lancaster, 1898[?] ("Digitized by Google")), (May 1899[?]) p. 510, ("Mary Mack dressed in black") (1 text)
Harold Courlander, _A Treasury of Afro-American Folklore_, Crown Publishers, 1976, pp. 535-536, "Mary Mack" (1 text, 1 tune)
Gwenda Beed Davey and Graham Seal, _A Guide to Australian Folklore_, Kangaroo Press, 2003, p. 151, "(Mary Mack)" (1 short text, described as a handclapping game)
Ron Young, _Dictionary of Newfoundland and Labrador_, Downhome Publishing Inc., 2006, pp. 225-226, "(Miss Mary Mack, Mack, Mack)" (1 text, a handclapping game)
Tom Nash and Twilo Scofield, _The Well-Travelled Casket: Oregon Folklore_, Meadowlark Press, 1999, p. 59, "Miss Mary Mack" (1 text, a clapping game)
Roud #11498 and 10999
RECORDINGS:
Hunter children "Miss Mary Mack" (on JohnsIsland1)
Children of Lilly's Chapel School, "Mary Mack" (on NFMAla6, RingGames1)
CROSS-REFERENCES:
cf. "The Swapping Boy" (plot)
cf. "Turkey in the Straw" (floating lyrics)
cf. "Went to the River (I)" (floating lyrics)
cf. "Hi Ho! Skippety Toe" (lyrics)
NOTES [350 words]: Not to be confused with the music hall song of the same title, which involves what sounds to be a shotgun wedding. - RBW
Raudnitzky: "Once upon a time, now long ago, there lived in the city which we know as Gotham, two little sisters who were wont to amuse themselves with ... ['Mary Mack']."
One spiritual includes the verse "Look over there what I see, Mary and Mac, Dressed in black. Where shall I be when the first trumpet sound? Where shall it be when it sound so loud? Goin' ter wake up de dead" (source: Anna Kranz Odum, "Some Negro Folk-Songs from Tennessee" in The Journal of American Folklore, Vol. XXVII, No. 105 (Jul 1914 (available online by JSTOR)), #3 p. 257 "Goin' ter Wake Up de Dead" (1 text)). Apparently not knowing about the rhyme, Odum reasonably takes Mac to be a corruption of Martha, Mary of Bethany's sister (John 11:1-12:11); or perhaps he has it right and the rhyme is corrupted.
On the other hand, Archer Taylor in English Riddles from Oral Tradition (Berkley, 1951) apparently lists "Mary Mack all dressed in black, Silver buttons down her back" as riddle #656 with the solution "coffin" (source: Robert A Georges and Alan Dundes, "Toward a Structural Definition of the Riddle" in The Journal of American Folklore, Vol. LXXVI, No. 300 (Apr 1963 (available online by JSTOR)), p. 114).
Perhaps this should be named .".. Dressed in Black." Among the subjects are "Darby and Joan" -- having nothing to do with the "Father Grumble" take off -- or "Darby's son" and "Betsy Blue," both in black, with silver buttons down the back (Northall). - BS
There seems to be fairly standard clapping-game version of this now:
Miss Mary Mack, Mack, Mack,
All dressed in black, black black,
With silver buttons, buttons, buttons,
Down her back, back, back...."
But the many versions show that there was more variety in the past. Was there a media program that standardized it? I don't know.
Abrahams-JumpRopeRhymes agrees with Taylor's interpretation that this is a riddle for "coffin." I strongly doubt most players today would guess that -- or even guess that this is a riddle. - RBW
Last updated in version 6.5
File: CNFM158B

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