They used to play this cut on my local public radio station in the '80s (I think), and the woman who sang it had an unmistakable voice, but I can't remember her name! It's live--you can hear the audience laughing--and she leads in with a little spiel about when to sing the song. Something like: "It's four o'clock in the morning. The baby is still crying. The paregoric is gone. It's gone because you drank it. That's when you take a deep breath, smile, pick that baby up in your arms, and, in your softest, kindest voice, sing 'The Hostile Baby-Rocking Song.' "

Oh, this is the day we give babies away
With a half a pound of tea.
If you know any ladies who want any babies,
Send 'em around to me.

Oh, this is the day we give babies away
With a half a pound of tea.
You open the lid and you take out the kid
With a written guarantee.

I think there's a third verse that slipped my memory.