Here's what I learned in San Francisco around 1990 in elementary school:

Down by the banks of the hanky-panky
Where the bullfrogs jump from bank to banky
With a hip, hop, hippity hoppety
East side, west side, kerrrrrplop

That was done to a circle elimination game as described in some other posts.

A few years later I learned a slightly different version from some kids at day camp, also in San Francisco

Down by the banks of the hanky panky
Where the bullfrog jumps from bank to banky
With an eeps, ops, soda pop
Frog missed the lily and he went kerplop (freeze)

This was done to a 2-person handclap game which I can't really describe because it had some complicated motions. You did the same hand game, sometime right after or right before this other rhyme to the same motions. The lyrics to that one:

Bo bo, say yotton cotton
Nay nay, you are so rotten
Itty bitty cocoa puff
Bobo say yotton cotton BOOM (freeze)

Both of these rhymes had tunes that went with them.