Here's an explanation of one way this rhyme is played:

DOWN BY THE BANKS
"I grew up in Pittsburgh (went to Liberty, Frick, and Schenley {High School} c/o 2000)
I know a circle hand clap game with chants called: Down by the bank. It is an elimination game because the children stand in a circle and try to eliminate (or not get eliminated) at the end of the song. The setup is that both of your hands are palms up. Your right hand is under the hand of the person next to you and your left hand is in the palm of the person next to you. When your right hand gets tapped you tap the hand in your left and return your hand to the resting position. To be eliminated if the last note of the song gets on you and you are to hit the hand of the other person and fail to do so before they pull their hand away you must leave. If the person whose hand is to be hit gets hit, they are eliminated. When only two people are left they alternate their wrists until the game is over and then arm wrestle to figure out the winner.

The words start:
Down by the bank with the hanky panky
Where the bullfrogs jump from bank to banky
Singing eep opp orp opp

-snip-

Source: Flojaune G. {Pittsburgh, Pennsylvania}, electronic mail to Azizi Powell, August 2004