Check with your local roofing supply about one of the self-adhering granulated "modified membrane" systems. They come in rolls.
There are flashing details involved, but basically there's a nailable base that you install over the wood deck, then the self-adhering "cap sheet". I won't try to explain it all here, but any roofing store I'm familar with would be happy to provide you with instructions, and advice/tips. It's the kind of thing that can be long-lasting and durable, plus should be easy enough for a "construction-minded" handy person to install,