Thank you so much for posting this!!! I went to an all black elementary school in Norfolk, VA in the early to mid 70's and we used the variation you described (shown below).

"The confrontational action in these verses follows a consistent pattern. First, these rhymes are almost always given from a female perspective {which makes sense since the person or persons reciting these rhymes are usually girls}. Secondly, in the rhyme, a Black {or "Colored"} girl rejects the advances of a White boy. Thirdly, the girl tells the White boy that she "likes a Black boy and he likes me". And fourthly {if there is such a word}, the girl threatens to get a Black {or "Colored"} boy to "beat his {the White boy's} behind".

"I have also found or received an example of this rhyme in which a {presumably} Black girl tells another girl "Step back white girl you don't shine/I'll get a black girl to beat your behind". However, I have never found or received any version of this rhyme in which a White girl or White boy initiate this confrontational encounter."