Many sites replace their icon using a unicode character. Chess.SE uses a rook ♜, Poker.SE uses a club ♣, and so on. I believe it's possible to do the same here.
I understand the restrictions are just "it has to be a unicode symbol". There's some good options:
- star and crescent: ☪︎
- the Kabaa: 🕋︎
- a mosque: 🕌︎
- Allah: ﷲ
[There's "woman in headscarf", but it's probably best to avoid it because of "image making".]
The more unicode savvy amongst us might be able to give advice on the different versions of these characters.
Just be aware that it most cases it's going to be displayed very small. It mainly shows up on the hot network questions list and your flair. E.g. here's my flair (the Islam.SE icon is after the math.SE icon):
We should be able to change the "IS" into something more Islam-related.
Question: Should the Islam.SE icon (currently "Is") be changed to something Islamic?
This would be a temporary change, until SE fully designs the site. However, given the sheer number of sites waiting for designs, it may be a long time.