The story as I heard it was by Jerry Clower and could probably be found on one of his old recordings. It involved giving the monkey a revolver and a flashlight, allowing it to climb the tree, find the coon, and shoot it.
It seems that the dogs indicated they had a coon up a tree, the monkey was sent up with light and revolver, looked all over for the coon, and upon not finding the coon, descended the tree and shot the "lying coon hound."
That's it, it was Jerry Clower.
Thanks...I just found it on iTunes and downloaded it. It's a 7 1/2 minute sketch, pretty funny.