I live in Melbourne Australia, and during the 90's I was also taught this version:
Down by the banks of the Hanky Panky
Where the bullfrogs jump from bank to banky
With an A, E, I, O, U (you), R (are), out!
It was a two person clap, that was quite complex with up, down hand motions and hand slapping, it also finished with hitting the other person on the head or chest, depending on how much you liked that other person, of course.
Until I read this post I had never heard of it done in a circle, it was also a school yard thing, never a taught/practiced in class experience.