One possibility is a monolithic coating of some waterproof substance like fiberglass. A problem with this approach is that fiberglass is not particularly sustainable or healthy to work with. It also would require exceptional technique to create an attractive looking roof.
I was browsing the aisles at our local Home Depot yesterday and came across rolls of thin aluminum used for various roofing tasks. Perhaps this material could be pleated and formed to wrap around gently curving roofs.
The images at the top show some experiments with paper.