In Streets of Laredo/St James hospital, I thought the cowboy was shot, not ill.

Ahem! Ahem!
Me mother has gone to church!
She told me not to play with you
Because you're in the dirt!
And tisn't because you're dirty
And tisn't because you're clean
It's because you have the whooping cough and eat margar*ine*

And then there's the one that ends

...in walked the doctor
In walked the nurse,
In walked the lady with the alligator purse!

Measles said the doctor
Mumps said the nurse,
Chicken pox said the lady with the alligator purse!

Out walked the doctor
Out walked the nurse,
Out walked the lady with the alligator purse!

We also used to play a variant of Tag called Yellow Fever, requiring lots of children over a large urban territory. Starts with one person being It and anyone they tag becomes It too and you don't know who is It and who is safe. Sorry, not music, but germane. Like the measles. Rue, bella! Ok, stopping now.