This was actually played today in class!

Down by the river by the hanky panky
Where the bullfrogs jump from bank to banky
Saying "East side west side east side west side"
Dilly Dang Dong!

This was always my favorite hand game, since we could do it with a big group of people! It has to be really fast though. In elementary school, some kids counted the number of beats or hand-slaps in the rhyme to predict who would get the last slap.
One teacher thought it was a gang song though, with the "east side west side east side west side".