Morey Amsterdam recorded this in the 1940's. As I remember it went :

A mother was washing her baby one day
Dear little mite, so slim and so slight.
The mother turned round for the soap on the rack.
She was only a moment, but when she turned back:
Oh where Oh where is me baby, she cried.
Oh where is me baby, and the angels replied:
Your baby has gone down the drainpipe.
Your baby has gone down the flood.
Dear little mite, so slim and so slight.
He should have been washed in a jug.
Don't worry your head, just be happy,
and remember he suffered no pain.
He drifted away down the plug hole.
Let's hope he don't stop up the drain!