This is a topic that we just had to decide for our flock, as we are building a larger coop and run... So I have been talking with friends who own chickens, as well as pouring over all the options on this website and others, trying to get the most effective solution without breaking the budget. Here is what I've found:
I've heard of people running regular twine across the run at about 1 ft intervals, and criss-crossing them, creating a woven effect to prevent anything from entering. Can get saggy in the middle - Not great for large areas for this reason. This won't keep out sparrows or other smallish birds, who can still carry germs and other undesirables into the coop, as well as eat up all the food, but it does keep out the bigger preditors like owls, eagles, hawks and vulctures. It is also fairly effective at keeping chickens in.
Some people use a shade tarp, but that is prone to collecting water or snow. Could be great if installed at a slant, though, just for shade? (and if the sides are "covered" somehow, to close up gaps) If attached well, it does a fine job of keeping other birds out and chickens in. Also prone to sagging in the middle.
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http://www.amazon.com/gp/product/B004HKIUAG/?psc=1&s=hi&ref=noref&ie=UTF8 )
I've also seen people using bird netting across the top. It blocks without collecting any snow or rain, the way a tarp would. It does keep out smaller and larger birds. It also costs much less than a tarp. Can get a little saggy in the middle, but since this is all one large sheet, a post holds it up nicely. (This is what we are going with, with a corrugated roofed area right off the coop for shade and rain protection)
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http://www.amazon.com/Easy-Gardener...8&qid=1350672216&sr=8-1&keywords=bird+netting )
Another method that looks very neat and durable is framed metal fabric that is attached to the sides, but that would probably be better suited to a wooden run with similar sides. It's also a lot more work, and more expensive.
I agree with earlier posts, though, that a shaded area would be a good thing, whether as a part of your covering or as a separate shelter under or over your bird-proofing.
Good luck!