Aluminum shingles from cans.
This reduces the waste stream.
Ceramic tile aka spanish tile
You'll have to do your research on the materials used in fabrication
Micro Concrete Roofing Tiles
here's a video
You can make them yourself.
Thatch
This can be done with organic material and has the advantage of being compostable when its time to replace it.
Glass
Consider covering the roof with solar thermal and PV panels