Lawyers, Guns and Money is a good song… I’ll definitely put it as one of my alternates at the least. 
If not The Man Song,
then How about paul Simon’s You CanCall Me Al or The 59th Street Bridge Song (otherwise known as “Feelin’ Groovy”)
Or Maybe * I Can’t Get Started (with You)*
I’d say “Science Fiction Double Feature” or any number of other RHPS by Richard O’Brien
if you have watched the show, which I imagine you have, then you know that it is more important to sing a song well at auditions then it is to sing a the perfect song.
Pick the song you know the best, feel most comfortable with, and don’t worry about what genre or category it is in…
FWIW, I think wearing “The Official Straight Dope” T-shirt would be an excellent idea…
“What a Wonderful World” for optimism and those critical vocal gymnastics.
“The Letter” by the Boxtops would work if you have a grittier voice.
And “Chin up, Cheer” up by Ryan Adams is as sunny as can be.
Or, if you’re up to it, why not kill 'em with “Break on Through” by the Doors?
“Closer” NIN. While staring at Paula Abdul. Especially during the chorus. At least you’d make it on the worst auditions show.
After I posted that, I started to have second thoughts. I mean, it is a good song, but it’s just two verses and a bridge, and then it trails away for the whole second half of the song. There isn’t really much there to show off your talent in a competition.
Plenty of other good Zevon to choose from.
Rio by Duran Duran
Just kidding…
New Song by Howard Jones
remisser:
Don’t take them too seriously. Rio by Duran Duran has become something of an in-joke on the SDMB.
How about “Pressure” by Billy Joel?
Hey, I was being serious. 
Another Saturday Night
or
Mack the Knife (it got hits for Bobby Darrin, Frank Sinatra, Louis Armstrong and others and it’s very upbeat)
Three Dog Night’s version of “Old Fashioned Love Song” (not many people seem to know it was originally an Paul Williams tune) is one song I’m mulling over as well.
The Robbie Williams version makes my pants happy 
I’ll second that one.
I’d like to see someone sing “Michael” by Franz Ferdinand. That’s a pretty upbeat song, IMHO.
Robbie Williams also did a pretty cool song called “Old Before I Die” (I don’t know if it’s a cover, but I like him doing it). It’s really nice and upbeat as well.