This wasn't a single resize, but it should work fairly well. I used Photobucket's resizing features first to resize it to 256x256 and then to 64x64
EDIT: hm, I see that the transparency now has a few issues. Darn. Perhaps I could use a combination of Game Maker and Paint to fix this.
EDIT 2: It turns out that Game Maker worked the best, since it could resize the gif by itself. I then had to open it up in Microsoft GIF Animator and select each frame of the animation in order to pick the transparency color to use. Very tedius. The program called Pixie was very helpful here, as it allowed me to see the exact HTML color code of the background, which helped when trying to pick the right color out of a 256 color palette.
I was planning to export it as a strip, open the strip with paint and resize it, then import it back into Game Maker, but when I tried to export it as a strip, it told me that there wasn't enough space to do that. I've got 8 GB left on my hard drive... perhaps it was the fact that it was a bitmap. Anyway, this one seems to work, although there is a slight issue. It no longer has a simple 7 color palette. In order to make it look more pleasing to the eye when shrunk down, it now uses all 256 colors that GIF allows for. In essence, recoloring it would be nearly impossible. You could recolor the original and then resize it the way I did I guess.