(oh, look, I bump stuff)
Where is the love for Demon Woman? Out of all the season two songs, I find it by far the catchiest, the vocals are great and I love the rock feeling of it. And I'm a Bretero, mind you, so it's not just shirtless/leather Jemaine. It may not be particularly funny, but purely as a song it ranks up there with my very favorite Conchords songs.
Carol Brown is also quite a nice song, amusing and a good melody.
Third would have to be I Told You I Was Freekie. The video gets more hilarious every time I watch it, and the song also gets better with repeated listens. Shirtless honey-covered Bret also doesn't hurt.
I've never gotten the love for Sugarlumps, to be honest. There isn't much of a melody to it, what there is isn't all that catchy to me (it took me several listens to be able to even recall any of it), while the lyrics seem a lot more odd (leaning towards disturbing) than funny. Same with Too Many Dicks; I actually can't recall any of that.