I should add that this pergola is completely on top of the deck - so planting in the ground is not an option. I will need to use pots near each post on top of the decking.

Annuals only live one season, so you will need to take down the dead vines and replant every year. There are many annuals that would happily climb up the pergola: morning glories and their relatives moonflowers and cypress vine, climbing nasturtiums, scarlet runner beans, and many others. There will be much time, however, when the vines don't provide "cover" per se, because they need to be planted outside after frost (some can be started inside) and will die with the first frost. Good luck!

Many clematis grow happily in pots, but the pots must be LARGE - at least 16" or so I would think. But clematis are gorgeous, grow quickly once established.

Anything in pots will need an exceptional amount of watering, especially in the heat of July, Aug and Sept.

I have grown our native coral honeysuckle vine in large containers. It is prennial and has beautiful coral red bloom clusters off and on all season with heaviest flowering in spring and late summer through fall. Like gottagarden stated the plants will need an exceptional amount of watering. Could you plant at the base of the deck in ground and let your vines climb up to the pergola. If necessary, you could provide a short support from the ground to the base of the pergola to get them started depending on how high your deck is from the ground. There is very little leaf drop with honeysuckle and it is a wonderful hummigbird vine also.

Penny

morning glories and their relatives moonflowers and cypress vine may throw seed everywhere. I have cypress vine coming up in various places in my yard where it hasn't been planted for three years. Unless you actually want random reseeders, Cardinal vine which is a hybrid of Cypress vine would be a better choice for an annual vine as it doesn't reseed for us up here. It took two years to get rid of the morning glorie volunteers. Nasturtiums are gorgeous but they are an aphid magnet so you may not want those on a pergola that you will be sitting underneath. I had to rip out my naturtiums this year because the aphids were so bad. Scarlet runner been will also provide you with beans that you can harvest while the pods are still young. Another annual vine is Hyacinth Bean vine. It has purplish green leaves with pinksh purple flowers and deep reddish purple seed pods and is used by butterflies and hummers.

Penny

Clematis would be my recommendation b/c it is colorful and abundant and yet, lightweight. It is easy to cut in fall and it will just come right back in spring. It only blossoms for about 2 1/2 - 3 weeks though. If you need longer bloom time, you could mix it with two varieties that bloom at different points in the season. It's low maintenance (virtually none) and not too expensive either. My Dad has one that he cut down in August thinking it was done and after a couple of warm weeks late in August, it came back...with more blossoms!! (We never expected that!)
Best of luck in whatever you decide...I'm sure it will be lovely.

Thanks everyone. Couple of questions:

1. Will I need to take the pots of a Climatis inside for the winter, or will it survive in them?

Can you tell I'm new to this? :)

Clematis in the ground is very hardy but I am not sure how they would do in pots for the winter. You could double pot them with a layer of bubble wrap between the pots or pack peat most between the pots for added protection.

Penny