In my childhood we also had a couple of riffs that were sung to that tune but never considered as part of Polly Wolly Doodle:

Oh, there was a little nigger
And he wouldn't grow no bigger
So they put him in a five-cent show;
But he tumbled out the winder
And he broke his little finger--
Now he can't play the old banjo.

***

Oh, there is a little chigger
And he isn't any bigger
Than the head of a very small pin;
But the lump that he raises
Just itches like the blazes,
And that's where the rub comes in.

***

Of course, growing up in Maine, I didn't know what a "nigger" was and I didn't know what a "chigger" was.