A good comic song is a lot more than just telling a joke, or even a series of jokes, to my mind. It’s more about describing a situation and responses to it, (as in sitcoms and farces), but interlaced with clever wordplay, a consistent rhythm to the lyrics and both good and deliberately bad rhyming (ideally in triplets with the best saved until last, plus multiple internal rhymes, sometimes tortuous). Check out songs by George Formby, Victoria Wood, Jake Thackray, Miles Wootton, etc. for examples).