kryptonjohn:My initial idea is to screw polycarbonate roofing sheets to the underside joists. The joists run out from the house, and I plan to fix battens across them to create a fall, and fix spouting to catch it bear the house end.
If I can find it I'd probably use opaque sheets as it will probably get dirty and not look great underneath if it's clear?
This place has long-run steel under the carport, done by the same cowboys who did other work on the house. Based on that, (a) don't use long-run steel, and (b) make sure you have a really good slope on it so all the gunk that falls through the deck will actually be flushed off rather than building over time into a thick later of muck. Possibly consider providing access locations where you can flush all the debris and mould and moss out with a hose or water blaster.
Also, definitely use opaque sheets, you're going to get buildup of all sorts of stuff on there.
Finally, think about flexibility, if you're attaching it to a deck that's going to get walked over you need to provide some give to prevent cracking or fracturing around the screws where you attach it. The stresses in that case are going to be rather different than what you'd get from screwing it to a roof.