Adlumia Fungosa and Lofos are both great choices as far as patio climbers. Make sure that they are taken care of properly or they can cause permanent damage to your structure. Patio Covers generally require very little work to be maintained but being proactive is worth mentioning to prevent any unnecessary future costs.
Reply to Lily: I think both Suttons Seeds and Dobies sell plug plants by mail order. A Google search will find their web sites, and possibly other suppliers, too.
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Patio Covers Houston