A lot of David Bazan's (aka Pedro the Lion) work fits this. His solo album Curse Your Branches is a great example. The whole album deals with alcoholism, losing faith, and being a husband and father while dealing with it all. Even with that subject matter, songs like Please, Baby, Please sound like they could be in a Disney movie if you didn't tune into the lyrics. Bless This Mess is another song from that album that fits. Regardless of whether its what you're looking for, the album is amazing.