... the band ApologetiX. They take popular songs and lazily add christian lyrics, but I'm pretty sure they're being ironic. If not, then they're just unintentionally hilarious.
I checked out a few of their songs and got the uncomfortable feeling that they're actually serious. Someone actually took the Lambs song and wrote out the lyrics so you can see it's not a parody:
www.youtube.com/watch?v=DFOpO0IpcHw. To my ears, they're pretty cheesey lyrics, but that's just my taste. That, however, gave me the idea of looking for religious parody songs, but I haven't found any (yet) that are easily uke-able. A lot of take-offs on rap and modern Gaga-ish pap pop, but not too many that fit my sense of what is playable music.
There are a few groups calling themselves Heathens, but the best I found was The Band of Heathens. If that's who you mean, they're great. Can't find any atheist songs in their videos, however. But great acoustic sound.
Still looking, but found a few that might work: Godless and Free:
www.youtube.com/watch?v=wubIeiLs0qM which apparently comes from a book called Blasphemy! Anthems for Atheists (have to order one - Amazon has them in stock). And this:
www.youtube.com/watch?v=f-EsNX3MVyI&feature=fvsr. Also there's a band called Bad Religion with quite a few songs on YouTube, but they're geneall head-banger tunes that don't translate well to a uke.
Me. I'd prefer something lighter, a bit funnier, not an angry screed or a philosphical tract.