I have a few;
Pack Up by Eliza Doolittle; Often I stress probably a bit too much about what people think of me, and in the past people using homophobic slurs, 'jokes' and stereotypes used to make me feel kind of nervous, so on those occasions I did find the lyrics to this song pretty reassuring, particularly the lines;
'And when you're stuck in an angry crowd/They don't think what they say before they open their mouth/You gotta pack up your troubles get your old grin back/Don't worry 'bout the cavalry/I don't care what the people may say/What the people may say about me'.
That, and it's really catchy too.
Fix You by Coldplay; Sometimes you just have really rubbish days and on those days I find this song just hits the right spot somehow.
Born This Way by Lady Gaga; Enough said, really.
All-Star by Smash Mouth; I didn't know this song was from Shrek until my brother told me, and proceeded to bombard me with memes to the point where it's getting harder and harder to listen to this song without thinking of Shrek/Robbie Rotten/Bee Movie memes. All the same, it's still a song that makes me smile, if nowadays sometimes for the wrong reasons.
Make Me Smile by Steve Harley and Cockney Rebel; kind of an old song, and maybe not totally 100% 'happy' if you listen to the lyrics closely, but the tune is so catchy and upbeat, one of those songs you can't help but sing along to, albeit badly in my case.
Heavydirtysoul by Twenty One Pilots; this really isn't a happy song at all, yet it's become one of my favourite songs in general and one I tend to listen to a lot when I'm feeling down. I'm not sure why, just something about the overall tone helps me feel a bit 'stronger' sometimes. Overall I find Twenty One Pilots' songs good for when I just want to wallow a bit as well.
One Day Like This by Elbow; It's just a really happy, uplifting kind of song that has good memories attached for me, reminds me of sunny mornings, which the song itself kind of mentions.