Hello- I stumbled upon this as I was looking for the "correct" rhyme to sing with my 15 month old. I was delighted to find that everyone seems to have a different version. The one I remember growing up with in Northern Virginia is:
Down by the banks of the hanky panky
Where the bullfrogs jump from bank to banky
Singing ooh ayy ooh ayy
Skiddle I diddle I ding dong!