Here's my vote for suggested covers:
 
U2's " With or Without You" or the lesser known U2 song  "Hallelujah Here
She Comes" from the Desire EP.
 Plus, I second the thought of a studio version of the Replacements,
"Here Comes The Regular".  When you want to be bummed out and listen to
some music for the mood-- that's a great one!
Quick thought-- what about REM's " driver 8" or  "Gardening at Night"?
 
Jack
--sometimes I get the feeling things won't fall apart, then again.......