A friend of my mother's has a beautiful rose vine that twines over her portico. She said as long as she deadheads it keeps blooming all summer and even into the fall.
I'm partial to clematis vines, which are also non-invasive and darn hardy. And I believe their is a variation of the hydrangea in vine formation that can make it through humid summers and cold winters up here.
The berries are blue, pink, & white and glossy like porcelain. I bought it in 2003 and it never did much; then one Fall (2007) I didn't get time to clean off the chain link fence before winter. The next spring (2008) I found that it grows on old wood. That was the year it went over the top of the pergola.
The berries are small so way back against the chain link fence . . . they were hard to see..well last Sept they were over the top and inside the pergola and you could really appreciate their beauty when passing through.
Last Fall, I deliberately cut it back to the top of the chain link fence because I thought if let go, it might get too heavy on the wood structure. This Fall, I'll be braver and leave it alone to see how it does next year. I can always hard prune it if it seems too much.
I don't recall it being messy but maybe I just didn't notice; we walk through that pergola coming and going daily. I notice on my daily walks throught there more mess from spent clematis and lilies. I like to dead head the lilies and daylilies to keep it looking nice but don't even try to do that with clematis.
I use hybrid honeysuckle vines (Coral Trumpet (red/orange), Dropmore Scarlet (orange/yellow), and John Clayton (yellow). They do not self seed either by dropping or birds. I then plant a clematis with them. The hummingbirds love it and although it blooms heavy in spring - it continues to bloom on new growth all summer. I've attached a picture of the Dropmore Scarlet with a Jackmanii Clematis. I cut the honeysuckle back this spring so it isn't as large as usual. Sweet Autumn Clematis will vine to 30 feet and takes little care. I had it on a pergola that was mostly in the shade and it still did well. It does sometimes self seed and spread but I've never had problems controlling. It just started blooming today.
Your pergola looks beautiful! A private nook for a cup of tea or glass of wine?
I've never bought from this site, but always wnated to. Check out the roses! http://www.gardenvines.com I love the blaze roses and they're on sale! Pretty and a bargain. Check out the one called American Pillar too (cool photo)
Honeysuckle is an option, just be careful not to get anything invasive. I bought one with a great smell, delicate yellow and pink blossoms that sent nasty, woody runners out into the yard.