Boys and girls played Chinese Jumpropes at Whightman school in the mid sixties. A Chinese jump rope could be a cloth covered elastic you bought somewhere, or a chain of what we Pittsburghers call "Gum Bands", and the rest of the U.S. calls rubber bands. I remember it as a sort of giant cats cradle, where the jumper tried to make patterns with the elastic, double diamonds, etc. I don't remember any sort of rhymes going with it.
I do remember a regular jump rope rhyme,
Cinderella dressed in yella went downtown to see her fella
On the way her girdle busted, how many people were disgusted.
One, two three four............