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.
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.