I use to sing “Down by the river” that went.

Down by the river
with a hanky panky
Saw a bull frog
jump from bank to bank
he said, “E-I-O-U
Your momma stinks and so do you”
King Kong, donky kong
went to school with nothing on
asked the teacher what to wear
poka dotted underwear
not to big
not to small
just the size of the
broward mall

You sat in a circle and everyone had their hand on the persons next to them.

I just know that there was one that went something like

My name is L-I-L-I
jiggle I jiggle I
bomb bomb booty
chinese checkers
ani-ani freeze.

Anyone remember that one?