According to The RadioGOLDINdex, the song is called THE LAMENT OF HOMER TRACY, and it was sung by Bing Crosby and Fred Allen on "The Bing Crosby Show," on CBS radio on May 17, 1950. Similar information is given at Steven Lewis' Bing Crosby Internet Museum, but it says the name of the program was "The Chesterfield Show."

I can't find any evidence that the song was ever published, performed, or recorded apart from that program, but a recording of the program apparently exists.

Radio Station KBRD (Olympia, WA) lists it on their playlist, with the same performers, but it doesn't say where the recording comes from.