I've heard of the "Diamond Dick" one, but not the others. I also heard, "Rosie had a chicken;
Rosie had a duck;
she put 'em on the table;
to see if they would--"

(chorus)

"Rosie had a bicycle;
the seat was made of glass;
When Rosie dared to sit on it;
it went right up her--"

(chorus)