Could you try the Clematis Armandii and put something like a morning glory on it? You'll need an equally fast grower to duke it out, but I have the armandii. I also have armandii with a vigorous climbing rose. No problems with either, except they both bloom in spring so I add moon vines and morning glories to the mix.

My neighbor and I both have Confederate Jasmine. It has been evergreen for us. One winter we had some wind and cold damage, but I just cut off the brown parts and it kept going strong. The white flowers are pretty and the smell is fabulous. It is a very pretty vine. Mine is 12 years old and still gorgeous.

My jasmine climbs up and around our gaslight in front. My neighbor's is covering the picket fence in their front yard. You almost can't even see the fence!

Two native evergreen vines:

Carolina Jessamine: Gelsemium sempervirens
Crossvine: Bignonia capreolata

A third native evergreen, or semi-evergreen, flowering vine:

_Lonicera sempervirens_, Woodbine

This is a truly beautiful native vine that blooms during azalea season. This Southeastern woodland native produces a profusion of red, funnel-form flowers; and it is a gentle climber. There are also named cultivars, one being _Lonicera sempervirens_ 'John Clayton,' which produces flowers of a clear, pleasing shade of yellow. _Lonicera sempervirens_ is an exceptionally fine addition to one's landscape and is available from high quality mail-order nurseries, such as ForestFarm, which lists several cultivars in its online and print catalogs, and our over-priced Southeastern plant vendor--Wayside Gardens.