Nirvana covered this song because of Kurt Cobain's fondness for the band The Vaselines. Cobain described it as "a rendition of an old Christian song."
Depending on the source, the song title may vary. For example, on The Vaselines album The Way Of The Vaselines
the song is listed as "Jesus Wants Me For A Sunbeam." On another Vaselines album, All The Stuff & More
, the song is shown as "Jesus Doesn't Want Me For A Sunbeam." On Nirvana's Unplugged
album, the song is listed as "Jesus Doesn't Want Me For A Sunbeam."
During MTV Unplugged Krist plays an accordian while Dave's on bass and Lori Goldston plays the cello.
(Thanks to DN member Rich B. for his input.)