I have tried other types of tiles, but they don't seem to keep as cool as the granite. It won't hurt to experiment if you get some free tiles, though. Tile shops will often be willing to give you samples.
You can also chill granite tiles. Even when they're not chilled, they can keep pretty cool as long as they're in the shade. Sometimes if you go to the hardware store you can pick up damaged tiles for really cheap or sometimes free.
I take 2 liter bottles, fill them about 2/3 with water, and freeze them. I put the frozen bottles in with the birds, and they will lean up against them.
Make sure that they have plenty of water at all times. The breeze will help, more shade will help.