There is no reason to use PNG over GIF if you don't need the features PNG offers, like alpha-transparency or true color (as opposed to 256 colors, which is far more than that image needs). Nine times out of ten, gif will cut it just fine for avatars, since the difference of compression at that resolution will be meaninglessly little compared to gif. And contrary to popular belief, there are no longer ANY patent issues involved in the use of gif images, so don't even try that one.
I could re-compress my own avatar as a png image and save a quarter of a kilobyte, but it would be completely pointless, as the gif compressed image is adequately small in file size.