There is a book published by the Klutz publishers that has "Chinese" jump-rope games. There are many diffferent routines and My kids and I have lots of fun with them.. No rhymes though. When I did this as a kid in Connecticut (70's) we didn't do any rhymes just a lot of fancy footwork. The rhymes we used were for hand jives or jump-roping.

Jump rope rhyme:
Teddy bear, teddy bear turn around,
teddy bear, teddy bear touch the ground,
teddy bear, teddy bear show your shoe
teddy bear teddy bear, good for you!

Keep on playing!