Stumbled on this because I was remembering the "I like coffee, I like tea" clapping rhyme, and wondering what the ol' Mudcat had to say.

I went to elementary school starting in 1980, in Bloomfield, Connecticut (adjacent to Hartford). The girls (including my sister) did clapping games on the bus everyday it seemed, and when they hung out in the street, etc. Demographic note: my family is White; Blacks (including many Jamaicans) are a majority in the town, and were most of our playmates.

The version to this one went:
"I like coffee, I like tea
I like a Black/White boy an' he likes me
So step back White/Black boy, you don't shine
I'll get a Black/White boy to beat your behind."

The girls would switch the race of the boy, depending on who was singing. Sometimes there'd be confusion if a White and a Black girl were playing together, and they'd sort of get jumbled up on that word and try to push their version. Sometimes they would agree on a skin tone based on a previous conversion about who the girl whose "turn" it was actually "likes." The reason why I remember distinctly that they did it both ways was that as a little kid I tried to imagine what "you don't shine" meant. I'd try to reason what skin tone "shined" more! Needless to say, I never figured it out!