I sing goofy songs to my kids all the time. Generally I make it up on the spot and they tell me "don't sing that, daddy" through the whole thing.
I used to tease my wife with a regular jingle during football season. It would go something like:
Today is Wednesday, tomorrow is Thursday, next conems Friday, and then iiittttt's UUUUUU TTTTTTTTT Gaaaammmme Daaaaaayyyyy.