Actually, there are many. What zone do you live in? Of course I am prejudiced, but a rose I raised fits that bill quite well. Annie Laurie McDowell is extremely fragrant, shade tolerant, completely thornless, very disease resistant and flowers year round in Valencia and Encino California. Here are photos of it on Help Me Find. She's a joy to train and dead head because she doesn't bite! She's available from Burlington Roses with more sources coming along in spring. As with many continuously flowering roses, it will often flower at the expense of growing so if you want it to climb faster, prevent it from blooming to encourage more growth, faster. Kim

Here is a link that might be useful: Annie Laurie McDowell on HMF

And to top all that off ALMD is gorgeous! Unfortunately the small band I got a few years ago didn't make it through it's first winter. I'm really glad to hear it's going to be more widely available soon, Kim! I've been wanting to replace it!

Compassion, ClairMatin, Dublin Bay, Quadra, Dawlow's Enigma, Ramblin Red, Berlin, Royal Sunset, Autumn Sunset, Fourth of July, New Dawn, and many others I grow repeat bloom all season.

I wonder how Annie Laurie McDowell would do under high BS pressure? I have a spot just for a rose like this!!

Ramblin' Red is one of my only climbers that blooms all season without rests - New Dawn, Polka, Dortmund, St. Swiftun, Abraham Darby, Autumn Sunset, Westerland, America, Antique, Roseanna, Rosarium Ueterson (sp?) all bloom in flushes with rests between for me. This was taken early in the season - it was well over the top of the arbor by late summer, but always seemed to be in bloom.
{{gwi:222734}}

Big K, which ever rose you choose, make sure it is hardy for your zone. What works well in Southern California or Florida won't necessarily be a winner in zone 6.