Star Fucker (Star Star) by the Rolling Stones. Oddly apropos for American Idol.
Oops, made the wrong link
SSG Schwartz
“The Latin One”, by 10,000 Maniacs. Cheery, 80’s poppy song about the horrors of a gas attack in the trenches of WWI. Adapted from a poem by an English fellow who died in that war, if memory serves.
Oh, and almost anything by Voltaire. The goth singer, not the French philosopher, naturally. “God Thinks”, “When You’re Evil”, “Zombie Prostitute” - hell, just pick a song at random. The only one that would probably be allowed on is “Goodnight, Demonslayer”.
I meant to say H.W.C by Liz Phair. The lyrics are NSFW, but don’t hum them and you should be OK.
SSG Schwartz
ooooooooooooooooooooooh “She Bop” by Cyndi Lauper
and
“If I Were Gay” by Stephen Lynch.
Although that may have been an appropriate song for Clay… 
Cause they couldn’t do it as ‘well’.
“To Drunk Too Fuck” by the Dead Kennedys. Great, great song, but can’t do it on TV.
Oh, well if Stephan Lynch songs are allowed. I’m gonna go with Special Ed, or Taxi Driver, or Talk To Me. How about Asshole by Dennis Leary.
Kill all the White People! - Type O Negative
(which I snuck into the video introduction of my high school news program)
“Closer” by Nine Inch Nails
“White Punks on Dope,” by The Tubes. (Actually, I’ve never seen “American Idol,” but I’ve heard about it.)
“I Dig Rock and Roll Music” - Peter, Paul and Mary
FTR, I’ve never watched but a few minutes of the non-audition shows, and even then only a few.
Cousin Kevin’s the bully cousin. The molester is Uncle Ernie, who’s the narrator of Fiddle About.
I doubt they’d have any trouble with Anniversary, either. And he has a couple I wouldn’t be more than slightly surprised to hear.
Others of his that would Totally Not Make The Cut, however - The Man Upstairs, Dead Girls (how many artists have two songs about necrophilia?), The Headless Waltz. Ex Lover’s Lover, The Chosen, or The Last Word.
I think most of The Dead Kennedys’ oeuvre would be off-limits: “California Uber Alles”? “Holiday in Cambodia”? “Kill the Poor”? “I Kill Children”?
Although I love the image of someone getting up on the Idol stage and roaring the words “God told me to skin you alive … .” 
And how about Gil Scott-Heron’s “The Revolution Will Not Be Televised” … ?
The Roof is on Fire - Bloodhound Gang
The Bloodhound Gang? Could you really limit it to one song from a band with an album called Hooray for Boobies? Althogh, I’d really like to see someone tackle A Lapdance Is so Much Better When The Stripper Is Crying.
Failing that, another song we’re not likely to hear on Idol is Pink Floyd’s Not Now John. I think every third word or so is “fuck.”
Crazy Bitch - by Buckcherry
Though Omer in the movie “American Dreamz” performed the more traditional, Frank Sinatra “My Way” at the end.
Oh this is going to be fun:
Everything by Big Black. Any band that can have songs about child molestation (“Jordan, Minnesota”) and self-immolation (“Kerosene”) on the same album is doomed never to be on AI.
Tons of Frank Zappa, but especially “Dinah Moe-Humm” and “Jewish Princess”.
“Me and a Gun”, Tori Amos
“Polly”, Nirvana
And the song most guaranteed to have the studio audience burn down the entire building in protest–“Rednecks” by Randy Newman.