This is always an interesting project because, usually, the Homeowner wants to keep the bottom deck dry. Well, short of building a peak-roof on top of the patio (first), THEN build your deck, you don't have too many options.
The problem w/using tar paper is it's NOT meant to be continually 'exposed' to the elements (or Mother Nature.) Over time, it will dry out and crack and crumble on you, and start leaking. What you might want to consider is some corregated sheathing. This will 'catch' the water that runs through the upper deck and 'channel' it to one side, or end (whichever you choose.) Use an all-weather material since you probably won't have access to it once you build the deck. (ANd use screws when attaching your decking material to the joists, if that's what you're doing. Use screws wherever you can.)
Once you've managed to channel the water, now you need to route it off of the sheathing. YOu'll need to plan for a gutters and downspouts. THEN, once it leaves the downspouts, you need to keep it away from the rest of the structure.
Others may have other ideas. My best to ya and hope this helps.