Some of the ones I recall from the mists of antiquity in Brooklyn:

I should worry, I should care I should marry a millionaire He should die, I should cry I should marry another guy.

I should worry I should fret I should marry a suffragette.

My mother gave me fifty cents To see the elephant jump the fence It jumped so high it touched the sky And didn't come down till the fourth of July.

(and my pet)

Marguerite, go wash your feet The board of health is across the street.