These came from my grandmother who was born in 1883. (And was 34 when she gave birth to my mother, who was 38 when she gave birth to me. I'm not THAT old.)

Mary had a little lamb
A little pork
A little jam
Some ice cream soda topped with fizz
And oh how sick our Mary is.

Once a mig policepan met a biddle lum. Hitting on the burbside eating baba rum. Said the mig policepan will you simme gum, "Ninny on your tintype!" said the biddle lum. (Ninny on your tintype was a rude way to say no.)

From my mother, who swore she saw it in a toilet stall somewhere.
When you're using our john
Don't stand on the seat.
Our crabs can jump
up to 15 feet.