Just because a song has a good (positive) message doesn't mean it's a good (quality) song. As a missionary for the LDS church I learned a lot about presentation. If our presentation was sincere, respectful, and exciting enough without being overwhelming, strangers were more likely to set aside their reservations and hear what we had to say. Too blatant, and we push people away. In the art world, anything created by an agenda becomes transparent. That's why blatantly political songs drive me insane. The artist is more interested in propaganda than in throwing a party for your ears.
The same is true for songs with a positive message. I get plenty of sermons every week at church--good ones, when I'm ready to hear them. I can tell if you're giving me a sermon when you compose, and most everyone else can, too. If you want me to subscribe to your philosophies or agendas then I need to feel them, not just hear them. I quote Orson Scott Card:
So much of Mormon art shows good to be bad! That is, it often shows goodness to be puerile, or impossible, or--heaven forbid--boring. A gooey G-rated film that reduces goodness to niceness does as much harm as an R-rated film that makes evil seem rewarding, since both will move an audience to shun the good and espouse the evil. (A Storyteller in Zion, Bookcraft, p.102)
I've talked already about a few recent attempts at happy songs that show room for improvement. So what makes a positive song appealing?
It needs to tell a story
I don't necessarily mean a narrative. There should be a defined situation and the singer should either relate the situation to us, or play a character in the story. Like maybe a best friend giving advice. A good example: "Tell Her About It" by Billy Joel. He gives pointers to someone else, hoping he doesn't make "the same mistakes I made." Now we know where the singer comes from, and what gives them the right to tell us anything.
A Positive goodness/badness ratio
Tolkien's The Lord of the Rings ends it's main conflict about 3/4 through the 3rd book. A lot of hardships go down up to that point, and Tolkien apparently wanted to emphasize how much better things became for Middle Earth and how much the journey was worth to everyone. Let there be sadness in the song, let it make the song interesting, but let the happiness or solution outweigh the problem. Think of "Hey Jude" by The Beatles. For every line mentioning sadness, pain, or fear there are at least 2 lines to cheer Jude up, not counting the 4-minute Na-nas.
Focus your energies
Let's go back to Billy Joel. His wrote a blatantly positive song called "You're Only Human (Second Wind)." It feels much more bland and generic than his other songs because he throws in all kinds of similes and topics at once. Beginning with someone coming down on himself for his mistakes, he talks about crashing into stone walls, boxing, heart break, and getting your "Second Wind." He could have condensed the song to wind metaphors to stick with the song's title. Toward the end he mentions catching his breath and facing the world. Maybe something about kite flying? waiting for the breeze to pick up so he can fly again? It would have felt more complete and coherent as a result.
Use religion sparingly
These days there are enough Atheists and skeptics who tune out at the mention of any Deity, especially Judeo-Christian. I don't mean to deny or shy away from what you believe, but use care in bringing up religion as the source of your beliefs. Too many songwriters believe you just mention God and the audience will come in droves to hear what you have to say. If I hear a decent song only to discover that it was sung by The Fray, I think twice about listening to it again. Same goes with religion for some people.
If God Himself is the subject of the song, then you're writing a religious song, rather than a plain positive song. That's a separate category altogether, with it's own set of guidelines.
If there are any more guidelines to add to this list, I'm all ears. I got an idea while I compiled mine, though: I've harped on songs before, picking them apart for what's bad, but I don't usually risk putting my own creativity on the line. If I can't do any better, why waste my time tearing something down? Coming soon, I will attempt to re-write lyrics of famous songs, in the hope of making them worth their fame.