The guy in this song is declaring his love for his wife, Marie, making his pitch with some bad, but heartfelt, poetry:
You're the song that the trees sing when the wind blows You're a flower, you're a river, you're a rainbow
Unfortunately, the only time he'll tell her he loves her is when he's drunk. The rest of the time he's a heel.
This song is part of Newman's Good Old Boys album, which tells the story of a guy in the American South from his point of view. We meet Marie in the song "Birmingham," where we learn about their life in the Alabama city.