A clear plastic roof may be just what you need. You can get clear corrugated roofing at your local building supply store or try something a little different. The material in this photo is inch thick honey comb plastic from Tap Plastic.
Layering Up: A lot of pergolas will only have one layer of overhead beams say going in a vertical direction. One way of adding more shade and roofing to the pergola is to add another level of beams this time going in the horizontal direction as