A.f.a.i.k. you got 2 options when keeping the transparency:
- Resize the image or
- Use only 1 or very little different colours preferably with rectangular shapes (= good compression) and use the alpha layer for the colour variations.
or a combination of both...
Using 1 colour (white) and set mode grayscale makes it under 20kb still at full size:

Matching avatar :
