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R.E.M. gave us "If you believe they put a man on the moon! Man on the moon!"
And on the same album told us "Take comfort in your friends, cos everybody hurts, and everybody cries... sometimes." Also of note is "If you feel like you're alone / No, no, no, you're not alone" from the same song.
The song was written with teenagers in mind - Peter Buck noted that this is why the lyrics are so much less idiosyncratic and direct than REM's other songs, they wanted to get a clear message to teens struggling with the stresses of growing up that it's okay to feel sad sometimes and that it will get better one day. Actually, that doubles as a huge, happy Tear Jerker, come to think of it.
Another song with an It Gets Better theme is "Every Day Is Yours to Win" from Collapse Into Now. For bonus points on the Heartwarming scale, the song sounds almost exactly like Automatic for the People's "Find the River".
"Every day is new again Every day is yours to win And that's how heroes are made."
"Nightswimming" as well, if you combine CMOH with Tear Jerker.
"Walk Unafraid" is decidedly rousing for awkwardness and non-conformity.
At the end of the Green album is an untitled track (usually called "The Eleventh Untitled Song") — Michael Stipe, singing to his parents to comfort them while he was gone on tour.