I feel compelled to add my version. I learned it at Greenlake Elementary in Seattle, WA in the late 1980s.

Down by the banks of the Hanky Panky
Where the bullfrogs jump from bank to banky
with an eep, ipe, ope, opp
And they ease off a little with a Ker-plop.

I vaguely remember this being a circle handclap elimination game as described above.

I always thought that these rhymes were "alive" only on the playground, and transmitted from child to child, but now that I have my own child, I find that I am remembering them and singing them to her as I scour my brain for any kind of nonsense that might amuse her. Might there be two ways these rhymes are passed on? Although I bet the first time my daughter hears a version from her peers, it will instantly replace the uncool "mom" or "home" version.