Okay, this may have been a fever dream because I'm pretty sure I saw it while home from school sick one day...
So it would have been in the late 80s or early 90s, east coast America. It wasn't a show I'd ever seen before, I was just flipping through channels out of boredom.
It was animated in a sort of sketchy style, maybe watercolor-ish. Very simple but trippy backgrounds. Looked like it could have even been from the 70's or something. (Schoolhouse Rock comes to mind?)
The characters were mostly human, except one of them was this cartoony anthro alligator with hair and clothes.
And at some point, a song starts, sung by a deep-voiced Louis Armstrong-type singer while the little alligator character danced around.
The lyrics I remember clearest went "Sing it once, since it twice, oh I love it chicken soup with rice"
And that's all I got! It has haunted me for decades.
I've tried searching by the song lyrics or searching for cartoon alligators, but no luck.