Jesus Doesn’t Want Me for a Sunbeam is the title. As I remember the Unplugged album, Kurt explains that it’s a traditional Christian song that the Vaselines covered. Definitely the only Nirvana song out there that featured an accordion.
The “Christmas” number from the Who’s Tommy has one:
And Tommy doesn’t know what day it is,
He doesn’t know who Jesus was or what praying is.
How can he be saved
From the eternal grave?
My all time favourite was Big JC by absolute genius Birmingham rocker Steve Gibbons. He is my all time favourite “why was he never a star” musician. I saw him in London in the 1970s at the Roundhouse when he was bottom of the bill and he blew everyone off the stage including Eric Burdon. Unfortunately I lost all my vinyl music over the years but hopefully a Brit Doper has the lyrics.
the flaming lips have a song, “thank you jack white for the fiber-optic jesus you gave me.”
and wilco has “jesus don’t cry”, but jesus is sort of used in vain there, i guess.
and gangstarrs “conspiracy” has a verse like this:
The S.A.T. is not geared for the lower class
so why waste time even trying to pass
The educational system presumes you to fail
the next place is the corner then after that jail
You’ve got to understand that this has all been conspired
to put a strain on our brains so that the strong grow tired
It even exists when you go to your church
cuz up on the wall a white Jesus lurks
actually, a lot of 90’s rap mentioned a “white man’s god” or a “white jesus” disparagingly.
Probably lifted from Townes van Zandt, this being the Smashing Pumpkins. From “Lungs”:
Jesus was an only son, and love his only concept
Strangers cry in foreign tongues, and dirty up the doorstep
I have no idea. That full bit goes:
“Tell me I’m the only one
Tell me there’s no other one
Jesus was the only son
Tell me I’m the chosen one
Jesus was the only son for you”
Looking back, man, that song sure is overwrought (I like it at the time, more for the music than the lyrics). But as you said, this being the Smashing Pumpkins…
My Head Hurts, My Feet Stink, and I don’t Love Jesus - Jimmy Buffett
Another one: Moral Majority, by the Dead Kennedys.
“If Jesus don’t save 'til we’re lining your pockets
God must be dead if you’re alive”
I missed the obvious one. About half the discography of Creed.
“The obvious one” being the word “secular” in the title, I’d guess. Creed were a Christian rock band in both senses of the phrase.
But the xtian title is “Jesus Wants Me for a Sunbeam”, isn’t it?
Meaning they were a rock band and had the talent of a bag of rocks? (Note the name Creed.)
That would make sense, but I can’t say one way or the other. Some 'net searching is called for on that one.
Just popping in to say that the Vaselines song “Jesus Wants Me for a Sunbeam” (later covered by Nirvana as “Jesus Doesn’t Want Me for a Sunbeam”) is NOT a version of a traditional Christian hymn. Compare the lyrics (and tune) of the original “Jesus Wants Me for a Sunbeam” with those of The Vaselines.
Warning - first link plays an annoying MIDI file.
“Jesus and Tequila” by the Minutemen
Sarah McLachlan, “Building a Mystery” And a cross from faith that died before Jesus came
Billy Joel’s “Goodnight Saigon,” a song about the Viet Nam war, includes the line:
“We dug in deep and shot on sight and prayed to Jesus Christ with all of our might.”
Jaay–ay-ay-ay-zus Christ–
Deny yer maker…
I used to cover this song in one of my bands. I loved jamming out on this one. 
The Ballad of John & Yoko
“Christ, you know it ain’t easy
You know how hard it can be
The way things are going
They’re gonna crucify me!”
Frank Zappa, “Jesus Thinks You’re a Jerk”.
Ah-ha. So basically the Vaselines did a takeoff on the title of the song, and Nirvana covered it. I think Kurt’s semi-exact words were “This is a Christian song, but we’re going to do it the way the Vaselines did it.” Not very clear, but sorta accurate when you know what the deal is.