Without seeing your deck I can’t give you specific construction advice, but I can tell you that a roof over an open deck (more properly called a verandah) is a terrific thing. It’s a shame that more decks aren’t built this way initially, since a roof adds so much. Besides extending the use of the space into rainy days, a roof greatly increases the life of any wood finish you apply.

Composites don’t have the same structural strength as real wood, so you’ll need to use lumber for the posts, rafters and roof boards of any structure you build. If you finish these parts before assembly, it’s much easier than painting over your head after construction. Since the underside of the roof structure is shaded, the finish will last forever. The finish on the underside of the verandah roof I installed at my place 15 years ago still looks like the day I sprayed it on. Other than cedar, pressure treated lumber works well. I used planed pine board for the roof of my verandah, laid over the rafters. This looks much better than the plywood that’s sometimes used for this purpose.