convert to a gif -- it limits the amount of possible colors. and you have control of that limit, anywhere from 2 to 256. i'd recomend something in the ballpark of 12-32 colors. it abstracts the image a bit, but not so much you can't tell what it is.
i'd also recomend simply reducing the physical size of the avatar.
this one, for example, is only 16 colors and less than 50 x 50 pixels, but still looks very sharp.
