When we got polycarbonate panels from the hardware store, the same aisle had a section with fasteners specifically for them (including some underneath support thingies for the waves, and peak bridge thingies for A frame roofs). We got the screws which have a rubber foam backing right behind the head, so when you drill through the polycarbonate and into the wood frame behind it, then the foam on the screw creates a seal against moisture as it's tightened.
- you can tell I have little technical knowledge, but we got it to work!
(then had to tear that coop down when we moved, now I have polycarbonate laying around that I haven't figured out how to reuse with screw holes in different places than the current need. Ugh.)