Thanks for the idea, Guest. 'Yellow Bird calypso' brings up things I've seen already.

Peter, that version is delightful. I love the beautiful a in 'banana' and the beautiful o in 'alone.'   It does have a nice 'flute' part in the middle, but the flute is playing the melody with trills. My friends would get bored if I hogged the melody while they merely played boomchick.

It's possible that what I remember is the (brace yourself) Norman Luboff version.

At the moment I have just finished listening to about ten versions of Yellow Bird on YouTube, and I need to drink some water and walk around for a while.