My cats get more terrible songs made up about them than any other creatures on the planet. Trevor and I are both extremely guilty (though I'm probably worse). The basic rules are take whatever song is in your head and randomly insert love for the cats. Only worry about rhyming if you really have to.
"There can be miracles, when you are fluffy. Though hope is frail, we love fluffy cats."
"Tonigh-igh-igh-ight, Julius is a cat. So let's set the world on fire. Because he's so good. And strong and handsome and orange."
"Tell me why-y. Tiberius is best cat ever. Tell me why-y. Tied with Julius and Fidel. Tell me why. We have so many good cats in our family. Cause I want to pet their soft fur."
"Hey, I just met you. And you're a good cat. So let me love you. And be my good cat."