BMI Repetoire lists "Caribbean Amphibian" as written by Joe Raposo and Mark Saltzman, published by Jonico Music, Inc. and "additional non-BMI publishers".
ASCAP's ACE Title Search only finds the song as an alternate title for a piece titled "Sesame Street Cues", ASCAP title code 498097100. It identifies the writer as Saltzman alone and the publisher as Sesame Street Inc..
The liner notes for Elmopalooza! (soundtrack) lists the song as written by Saltzman alone, publisher Sesame Street, Inc. (ASCAP) and copyright 1986.
I've added Sesame Street, Inc. as the publisher since two of the sources agree on that. I'm not sure what to do with the BMI information other than note it in Talk:Caribbean Amphibian.