Mme Alfred Carrier is basically thornless and very fragrant. Great rose in every respect. You climate is so different, I would not like to comment on resistance. Hopefully somebody close to you can comment on its health in your area. It is healthier than ZD here.
Olga

You should find and consult with your local rose society - they will be happy to share their experiences. If it was me, I would try banksiae lutea - the yellow form of Lady Bank's rose. It is COMPLETELY thornless, has no diseases that I have ever heard of. HMF says it is hardy zones 6b - 10b. It would cover the entire 12 feet length of your arbor. It blooms here from Feb or March through April, with some re-bloom in the Fall.

Jackie

I also hesitate to recommend anything because I too live in a different climate. Are there any nurseries nearby? They may be able to give you some idea about the health of certain varieties in your area.
I wonder if you would like Climbing Pinkie? Fragrant, thornless (or nearly so), I believe it is a climbing polyantha.

Both really good suggestions. I didn't really realize there were rose societies, so I will have to check. Thank you so much! There are nurseries around, but, I also know that some of the folks working them aren't always out in the yard with every particular variety of rose. We have another rose bush (not climbing) that has been suffering terribly with very extensive black spot (the old owner planted it under a birch tree, and it gets shade pretty early in the day). I've sprayed, and sprayed and sprayed. It's just not a good spot for the poor thing. I will be removing it in a few weeks and deciding whether or not it is salvageable. Since I will be planting the new rose in a much more sunny (most of the day) spot, that is also near some edible currant plants, which I grow organically, I would prefer to not have to spray anything on the rose if I can help it, as I don't want it wafting over to the fruits.

Golden Showers and Josephs coat both do well in San Francisco. San Francisco has more fungal problems then any place else in the world. We have more days of wet fog, then even England.

I'll put a link below to rose societies (rose gardening clubs) -- scroll down to see the list for California.

They give free advice, even to non-members, and can tell you which climbers would be best for your particular microclimate:

Here is a link that might be useful: list of rose societies in California

I have ordered St. Swithun (David Austin) climber, partly because it is supposed to be very disease-resistant and partly because it is very pretty (light pink). You might consider it also.

Kate

You might contact the folks at Rogue Valley Roses.
They're in Southern Oregon, so they might be able to suggest things that would perform best for you.
Their website is:
http://www.roguevalleyroses.com/

There is also Heirloom Roses, located in St. Paul, OR. They, too, may have good suggestions for you.
Their website is:
www.heirloomroses.com/

I wouldn't even begin to make suggestions to you on varieties, because I don't live in your climate.

My third suggestion would be to contact the members of Cascadia Heritage Roses Group, who may have excellent suggestions.
Since they're not selling anything themselves should have no particular bone to pick:

Jeri in Southern California

Here is a link that might be useful: Cascadia Heritage Roses Group

hi, I live in Kitsap County, very close to Puget Sound.

I grow Madame Alfred Carriere and have had no problems with pm. My Zeffy gets some bs at the end of the season but no powdery mildew so far. They are all two to three years old, so not mature. Zeffy is in a terrible spot, too, with poor air flow and morning sun only.

There is a large rose group in Tacoma, one in Olympia and a small one here in Kitsap County. Several in the Seattle area.