Here are a few I've had success with and my source for each.

Hopalong Peter (New Lost City Ramblers)
Watermelon Song (My Scoutmaster, John MacIntosh)
The Barnyard Dance (Carl Martin)
I'm Gonna Tell (Rosalee Sorrels)
Old Joe Clark, especially the gross verses:

I went down to Old Joe's house
He invited me to supper.
I stubbed my nose on the table leg
And stuck my nose in the butter.

Don't go down to Old Joe's house
I'll tell you the reason why.
He blows his nose on old corn bread
And calls it pumpkin pie.