I was attempting to find the words to the hand game I learned when I was young, after hearing my son sing the version he learned at school. I didn't see any version that was the same as mine but they are all very interesting.

I learned a couple of versions in the early 80's in Birmingham, AL. This is one that I think incorporated Japanese sounds:

Down the river of Hanky Panky
Bullfrog jumps from bank to bank,
Eesh, Meesh, Sun, Shee
Eece Say Meece Say Ding Dong
Your breath smells like King Kong!

I think it ended there. There might have been more, I don't remember if it was.

Today, this is what my 8-yr-old son sings:

Down by the river, Silver Rock
Michael Jackson wears no socks
Ee-pi-pi, Oh-pi-pi, Pow!
1, 2, 3, 4, 5, 6, 7, 8, 9,    10!