What about "My Unfortunate Erection" from 25th Annual Putnam County Spelling Bee? It goes up to an A, though. You could also do "I'm not that Smart" from the same show but it's a little bit harder to stage.
Or you could also do something from Avenue Q. You could do "What do you do with a BA in English?" or "If you were Gay".
"Shiksa Goddess" from The Last 5 Years is upbeat and funny, but the highest note is an A flat.
"All I care about" from Chicago! The highest note is barely an F.
You could do "Gaston" or "Me" from Beauty and the Beast. Both are really funny and both of them are in Vol 3 of the Musical Theatre Anthology for Baritone/Bass.
Speaking of Vol 3, there's a song in there called "I Hate Musicals" that I've never actually heard but the lyrics are absolutely hilarious. It also has a lot of speak-singing if that's your thing.
"Beauty School Dropout" from Grease. I'm not too sure about the range on this one but I highly doubt it goes too high. Bonus points for you if you do the final note in rock and roll falsetto!
"Dentist!" from Little Shop of Horrors is a REALLY funny baritone song.
I like "Always look on the Bright Side of Life" from Spamalot. And you get to whistle in it!
Since I dont know what your highest note is, I dont know which of these songs are an option for you, but I hope this helps!
Kiss Me Kate is a GREAT suggestion if you're really going for the "Lyric Baritone" sound. Especially since it requires more of a technique.
I suggest looking at Cy Coleman stuff... He wrote a LOT of comedic songs for men and since they're kinda older they don't expect you to belt B's... LOL For Example: Bigger isn't Better from "Barnum" I've got Your Number... Real Live Girl is VERY cute I'm a big fan of A Mover's Life. I want to say it's from "Little Me" but I'm not sure.