This house that I bought has a cover that was put on the deck with the use of 2 10 foot 4x6's, 3 4x4 posts, and a bunch of 2x6's hangered onto a 20 foot 2x6 ledger attached to the side of the house, and then covered with corrugated fiberglass.
The fiberglass leaks in a few spots, and i'm sure the spans are way too long for the lumber although I could be wrong, and it's got all kinds of crap growing on top of it anyway. . .
I'd like to tear it all down, make it just a little smaller and put a proper roof on it.