I learned this rhyme so long ago it seems.

I'm from GA, and my most vivid memory of playing this hand game was at girlscout camp in north ga. It was probably sometime around 1993-1995.
Our version was:

Down by the banks of the hanky panky
where the bullfrogs jump from bank to bank
you go eeps iips opes oops
chilly willy ding dong!

It fascinates me the number of variations on this there are. I had no idea! I sure do hope children still play these games - I have such fond memories