I like my Climbing Pinkie. Renae also does well here.
Renee

Check out the climbing roses on the web site for San Marcos Growers Nursery in Santa Barbara for some good choices for southern California.

Roses are going to be somewhat ratty in winter here, so the privacy won't be year round. If that is an issue, look at something evergreen. Also roses don't tend to be that dense (for complete visual privacy) unless they are massive growers, like say 'Mme Alfred Carriere'. How much room is there? Is it a matter of physical privacy (the prickles) or visual?

Something like a row of 'Skyrocket' junipers might be more effective, faster, and easier. Climbing roses (even here) can take 3-5 years to get big. A 'Lady Banks' would be fast, but it will also have the potential to rapidly engulf an entire house and yard, which can be a drawback.

One that might work, and also flower like crazy year round would be 'Secret Garden Musk Climber'. It grows very fast once the roots establish, and is fairly impervious to disease. You will have to look for a specialty rose grower that carries it, though. There's a big SGMC planted at Descanso.

Cecile Brunner is a big huge fast pink growing climbing rose. It even gets too big too fast, but if you want a privacy screen you can't beat it. It is like a weed, that can't even be stopped. I see it all over the place, taking over fenses.