Here are versions from B.A. Botkin, The American Play Party Song (Ungar, 1937, 1963, pp. 295-6), but not with a refrain.

                      POSSUM UP A 'SIMMON TREE

    Based on Negro songs of folk and minstrel origin.
    For A, cf. "Brudder Eph'em," Bass, JAFL, 44:430; "Cotton Field Song," Lomax (American Ballads and Folk Songs), p. 241; "Old Bob Ridley," The Negro Forget-Me-Not-Songster, pp. 155-157; Perrow (Eastern Northern Carolina, Mississippi), JAFL, 26:131-132 (two texts); "Karo Song," "Raccoon Up in de 'Simmon Tree," Scarborough, pp. 170, 172, 173; "Shake the Persimmons Down," Talley, pp. 34-35; White (Alabama), pp. 138, 236-27 (four texts).
    For B, cf. "Shady Grove," Combs (Kentucky, Folk-Say: 1930), p. 242; "Little Gal at Our House," Lomax (American Ballads and Folk Songs), p. 238; Perrow, loc. cit.; Scarborough, p. 177; "Possum up a Gum-Stump," Shearin and Combs (Kentucky), p. 38 (listed); "Possum uo the Gum Stump," Talley, p. 3; White (Alabama), pp. 237, 238, 239 (four texts).

                      A
(Sung by Orville Nicholas, Mountain Park, Kiowa County, from Cordell, Washita County.)

X:1
T:
M:2/4
L:1/8
K:F
A c c3/2 c/|A G F F/ F/|A c c3/2 c/|A3 G/ G/|
w:Pos-sum up a 'sim-mon tree, An' a rac-coon on the ground. An' the
A c c3/2 c/|(3AGG F F/ F/|A A G/ G3/2|F8|]
w: pos-sum said, "You son of a gun, Won't you shake them 'sim-mons down?"

                      B
                  OLD RACCOON
(Lois F. Beckham, Norman, Cleveland County, who played it at Memphis, Tennessee.)

Ol' possum in a gum stump,
Coonie in the holler,
Pretty girl at our house,
As far as she can waller.