"Go To Sleep Little Children" was written by Debi Spinney's father Gene Gilroy and originally performed on the 1996 Kathie Lee Gifford special "Lullabies for Little Ones". We're still trying to track down this version of the song from the special or album.
The version you heard last night on Muppet Central Radio is a bonus feature from the "I Am Big Bird" Blu-ray. It was performed at the Sesame Street Season 30 wrap party by Big Bird with Gene Gilroy on piano.
I somehow knew that song had some sort of a connection with that Kathie Lee special I mentioned earlier, but I never knew that it was written by Deb's father!
Additional note 1: One of the downsides of the Radionomy switch is that it no longer displays album/source information, meaning we have to go here if we heard something from some far-off source like "Little Children".
Additional note 2: For a few years now and just before Jerry Nelson died you've been playing these two song covers by him called "Daddy's Coming Home" and "I'll See You In My Dreams" which sound like voice-and-guitar demos for something that never materialized. How did you get a hold of those?