There were a whole range of Miss Suzie ones. They were the sort that you do while clapping hands with a partner in intricate patterns. The one Fiddler posted is one. Another (to the same tune) is:
Miss Suzy had a baby
She named it Tiny Tim
She put him in the bathtub to see if he could swim.
He drank up all the water,
he ate up all the soap;
he tried to eat the bathtub but it wouldn’t go down his throat!
Miss Suzy called the doctor,
the doctor called the nurse.
The nurse called the lady with the alligator purse.
“Measles” said the doctor,
“Mumps” said the nurse
“Nothing” said the lady with the alligator purse.
…I’m sure there’s more to that one but I don’t remember it.
And there was this hand-clapping one:
Miss Mary Mac, Mac, Mac
All dressed in black, black, black
with silver buttons, buttons, buttons
all down her back, back, back
She asked her mother, mother, mother
For 50 cents, cents, cents.
To see the elephants, elephants, elephants
Jump over the fence, fence, fence.
They jumped so high, high, high
They reached the sky, sky, sky
They never came back, back, back
Till the 4th of July, July, July.
This one was for chanting while skipping rope, no melody:
Cinderella, dressed in yella
Went upstairs to kiss her fella
She made a mistake and kissed a snake!
How many doctors did it take?
1, 2, 3 (keep counting skips until a miss)