XTC - Dear God (also covered by Tricky)
The Psychopomps - Godshit
Voltaire - God Thinks (except that end)
Quite a lot of Gary Numan
Public Image Limited
Bad Religion
Godsmack
Oingo Boingo - Insanity
The Flametrick Subs - Plastic Jesus (satire, that ending is great)
Front242 - Welcome to Paradise
Cat Rapes Dog - Hell is Real
Velvet Acid Christ - There is no God
My Life with the Thrill Kill Kult - Kooler than Jesus
Pretty much any of The Electric Hellfire Club
Roy Zimmerman does some good Atheist folk stuff
John Lennon - Imagine (even if he was a commie hippie fuck)
Look these up on youtube as I don't know who does them:
Why don't Bees go to Heaven
Skeptic in the Room
Rucka Rucka Ali - Let's go Jesus
That's all I can think of off the top of my head.
BONUS: Here are some hilarious christard songs that are totally serious and not satirical in any way.
Extreme Power - Respect and Obey Authority
Christian Side Hug
Jesus is my friend (a friend of mine?)
Source: DJ