There are a lot of words that rhyme with pig. Big is the most obvious, because that's what pigs are.
Another word might be dig, because pushing their snouts into anything and everything is pretty much all they do.
Gig also rhymes. As in "We've got a pretty good gig here. We roll around in the mud and people come watch us. What a life!"
How about wig? "I'm thinking of getting a wig, Supper. How about black, to match my behind?"
There's always jig. Maybe someday I'll sneak out and see these big guys dancing a merry ol' jig...but probably not.
Then again, to them, movin' around in a pool of muddy water is a jig, thank you very much!