you might want to try a mixture of moonflowers and morning glories, the glories will go ga ga if you take care of them, and the moonflowers will bloom at night and emit a wonderful fragrance. They are annuals though.

Jaimeg,

The Moonflowers and Morning Glories will be great choices for fast growing vines. You can easily grow them both from seed (there's plenty of time to get them started). Both of these vines climb via "twining" which means they wrap around an object for support and upward movement. I've found that they will twine around anything 1.5 inches or less in diameter. If you wanted to dierct them in a certain direction string may help. But keep in mind that they will want to grow up so you may want to direct them to lower areas to force them to fill in spaces on their quest to reach the Sun. One last thing. The flowers will typically point in the direction of the light so many of your flowers may be on the back (sunny) side of your trelis.

Good luck, Pat

In addition to the morning glories (annuals) and moonflowers (perennials often treated as annuals) there is the cardinal climber and cup and saucer vine.

The problem I have had with moonflowers is they are true perennials and in no hurry to bloom their first year. I have had large vines, but no flowers from them, but given my location in Wisconsin I have a fairly short growing season for them.

Morning glories and moonflowers prefer 'poor' soils which is hard to accomplish in a container. Not fertilizing at all will cause problems, but fertilizing in the right amount is also challenging. Consider growing both in the ground and simply not fertilizing them and letting them climb onto your deck via twine. I use empty milk jugs buried half way in the soil to grow them in. This keeps them free of other vegetation or being buried by mulch.

Cup and saucer vine is a moderate feeder and thus, in my opinion, easier to grow in containers as a little fert doesn't result in no blooms, just longer vines.

Cardinal climbers are fairly heavy feeders and like container life. Fertilizing simply results in longer, more lush vines and unless one goes insane with the nitrogen won't prevent copious blooms.

As with anything gardening related, your mileage may vary.

I have been thinking about this too. Justa, do your milk jugs have bottoms? Last year I grew morning glorys, moon vine, and cardnial climber. They all did fairly well. I grew them in plain dirt. Now I know better. I was planing on useing Al's mix. So I was thinking over what to do about they like poor soil thing. jaimeg don't mean to hijack your thread.
Morning glorys grow great from seed. Just nick them. I would buy the moonflowers. Because they take longer to bloom than mg. Cardnial climber is easy from seed and is beautiful. Cypress vine is nice too makes a nice screen. I'm growing all of these plus cup and saucer, purple hyacinth bean, scarlet runner bean, sweet peas and more. Good luck. Filix

Another fast growing vine (once it warms up) is ipomoea-sweet potato vine & also dichondra, annual vinca, creeping jenny (lysimachia). All of these should thrive, if you keep your containers watered & fertilize regularly...

Another good one is Black eye susan vine. It's a fast grower and comes in yellow, orange & peach colors. Easy from seed.
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Another-
Climbing Snap Dragon-
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Also (my personal favorites) Red Runner beans - pretty red flowers, and hyacinth Bean - comes in purple or white.
These are great! They are fast growers & you'll get lots of seeds from the seedpods for next year. The leaves are large so it gives good coverage.

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Here's a combo of Runner Bean (red flowers) & Hyacinth Bean - flowers not shown - although the leaves are in the lower right.
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Justa, do your milk jugs have bottoms?

No. These are borders more than containers. The vines grow right in the ground. The purpose behind the top and bottomless milk jugs half buried is that the area below my deck is sloped and mulched. The jug keeps the vine from getting mulch over it. If one were to grow in the lawn along a fence the jug would serve as a barrier to the lawn growing in and competing for water and nutrients.

I have personally grown vines on my porch for the same reason. It accomplished the purpose of cover, but they were all annuals and died in the winter.

I've used morning glories, moonflowers, and purple hyacinth bean. ONE purple hyacinth bean produced enough foliage to cover a trellis about three feet wide X seven feet tall. This year I will also be trying black eyed susan vine. Plants I would love to try but don't yet have include sweet potato vine and jasmine.

I've grown 'tidal wave' petunias against a chain link fence, and they grew over the top (3 1/2 - 4 feet). Passion flowers are also nice, but don't have enough foliage for screening, in my humble opinion.

I suspect that you only need a few core plants to provide the coverage you need for privacy. Then you will start adding other plants for fun.

Try searching and asking on the 'vines' forum. They can probably recommend some evergreens for your area.

-hydropetunia