Okay, so here's the original:

It's 37.81 kb, has 34 colors, dithering on, transparency on, and 8 animation frames.
And here's the downsized version, plus link:
http://i.imgur.com/daPrZlG.gif
It's only 17.85 kb, with 10 colors, no dithering, transparency on, and only 4 animation frames. (It was the same 4 frames repeated twice - cutting that down cut the size in half)
Hopefully it's small enough to work! If not, I think an admin can put it in manually, or if you want to make it even smaller, you'll have to actually lower the resolution itself. If you do that, since it's pixel art, make sure the downsampling is set to nearest neighbor, not bicubic. Let me know if there's anything else I can help with!