There's a good collection: Roger D. Abrahams and Lois Rankin, eds., Counting-Out Rhymes: A Dictionary (University of Texas Press, 1980). I'll quote the entry (no. 120).

Eena meena macker racker
Rare, ro, domino,
Juliacker, alapacker,
Rom, Tom, tush.

Opie (1969) [Children's Games in Street and Playground], 40-41, 53 [Scotland, England, Wales, Australia, New Zealand, since 1920's]. Eighteen variants, beginning "Eeny, meeny," "Eeni, meeni," "Iney, memey," "Ina, mina," "Eany, meany," "Ena, mena," "Eanie, meenie," "Eani meani," "Eny, meeny," and "Eena, mena." Discussed in relation to other gibberish rhymes. The rhyme is sometimes introduced with "I went to a Chinese laundry / To buy a loaf of bread; / They wrapped it in a tablecloth / And this is what they said." Three embryo forms of the rhyme are given: "Ena dena, dahsa, doma" (1909); "Eener, deener, abber, dasher" (1910); and "Haberdasher, isher asher" (1916) (see 123).
Turner (1969), 11 [Melbourne, 1920, 1962]. Two variants: "Eena, meena, micka, macka" and "Eeny, meeny macka racka."
Daiken (1949), 2.
Ritchie (1965), 45 [Edinburgh]. Two variants.
Those Dusty Bluebells (1965), 22 [Ayrshire]. "Eenie meenie macaracha, / A M dominacha, / Cheek-a-pop-a, lolly-pop-a, / Am bam bush."
Fowke (1969), 111 [Canada]. "Eeny meeny macker racker, / Rear ride down the racker. / Chicka poppa lollipop, / A rum tum trash."

~Masato