I'd look into the work of Mike Rayburn. He's not on Broadway but I saw him perform years ago and he's incredibly funny.
"All our dreams can come true -- if we have the courage to pursue them." -- Walt Disney
We must have different Gods. My God said "do to others what you would have them do to you". Your God seems to have said "My Way or the Highway".
A good clean comedy number, albeit a little corny, is "Confession to a Park Avenue Mother" from Herman's Parade. Cole Porter also has a lot of great comedy songs, that are only occasionally slightly dirty:)
Marie: Don't be in such a hurry about that pretty little chippy in Frisco.
Tony: Eh, she's a no chip!
Definitely second the Cole Porter suggestion. Although "The Tale of the Oyster" was originally written for a woman, I've seen it in various male compilation books and have used it to great effect!
"If there's any answer maybe love can end the madness,
Maybe not, oh but we can only try..."
If you are good at quick change characterizations, I would recommend "The Late Late Show" from Do Re Mi.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.
How about 'I Am Aldolpho' from Drowsy Chaperone? I know the song calls for a couple of lines from the Chaperone, but you could probably work around that.
"It does me no injury for my neighbour to say there are 20 gods or no god. It neither picks my pocket, nor breaks my leg."
-- Thomas Jefferson
Look up Rob Paravonian's Pachelbel Rant. It is more of a comedy routine than a song, but he does sing. And play guitar. It is about how he hates the cello part for Pachelbel's Canon in D and how he can't get away from the song (err chord progression really). Hilarious, actually. Not that you would want to copy his routine, but it might give you some ideas!
If you're doing a coffee house setting, "Taylor the Latte Boy" can be adapted quite well for a male, which also increases the humor. John Tartaglia's version is one of my all-time favorites.
"You're the worst thing to happen to musical theatre since Andrew Lloyd Webber!" --Family Guy
"Shut up! It's been 29 years!!!" --the incomparable Patti LuPone in her MUCH DESERVED Tony acceptance speech for Gypsy.
Kitzy's Avatar du Jour: Kitzy as Little Red Ridinghood in her college's production of "Into the Woods"
Checkout: Tom Lehrer, The capitol steps, Mark Russell, and (Live at the Crystal Palace - Aspen has multiple albums that are hard to find except for ordering direct) All the above are originally piano accompaniment, so you would have to arrange it for guitar.
For guitar based comedy songs checkout: Tom Paxton, Peter & Lou Berryman, Christine Lavin, Steve Goodman.
Peter & Lou: 1. "Your state name here" making fun of travelling musicians that try to win the audience over by mentioning their state in a song. 2. "Don't use the F-word with your mother" could be sung by a man defending his wife and so many more...
Steve Goodman: 1. Vegematic - About a guy who falls asleep with the TV on and what happens 4 to 6 weeks later. 2. "Talk Backwards" a tongue twister song about talking backwards. 3. "Watchin' Joey Glow" your son exposed to radiation. So many more... If you want to make fun of Cubs fans he has "A Dying Cub Fan's Last Request"
It has been so long I can't remember the names of Tom Paxton and Christine Lavin songs to recommend.
I am sure all the funny songs of The Chad Mitchell Trio, The Limeliters and Kingston Trio could be done solo. There are dozen of possibilites there.
check out Stephen Lynch's cds. If I remember correctly a majority, if not all, of his songs are done on guitar-mainly acoustic. And they're all very funny!