I used Corel Photo-paint (but any other decent graphics program will do the job). I took the original, cropped it to 192x192 and then resampled it to 48x48. Resizing looks a lot nicer when it's done by a simple fraction (e.g. 1/2, 1/3, 1/4, 1/5).
Then I first tried saving it as a 256-colour gif, but that was over the filesize. Dropping the number of colours to 128 did the job, and there doesn't appear to be any visible loss in quality. Oh, I told Corel to use an optimised palette (which means it looks for the best set to use, rather than a standard set or the first x unique ones) with no dithering on the image (so it used the closest colour).

Main points: resize by a simple fraction, like 1/2 or 1/3, and use less colours.