I sang this in Ann Arbor, Michigan, in elementary school beginning in kindergarten, 1957.

Down by the river, Mama she washed our shirts.
She liked to use a stone to knock out the dirt.
The river was shallow, the kids jumped about,
And when it's time for supper, Mama has to pull them out.
Don't go away; don't go away, Mr. River.
Won't you stop and play as you travel out to sea?
Don't go away; don't go away, Mr. River.
Won't you stop and play as you travel out to sea?

I feel like there were more lyrics, but can't recall them.