There's probably a few but I'd choose one that needs pruning at the same time as the rose.

Have a look at 'Clematis On The Web'. (www.clematis.hull.ac.uk)
They list loads of them and have good pictures too, by looking there you can spend as much time as you have and select one that's right for your position.

I was going to suggest Hagley Hybrid, which does well in that situation, but I think the combination of pale pink flowers with the yellow of Golden Showers would be pretty ghastly - have a look at one called Victoria - needs cutting down to about 8 inches in mid February, then will flower from late June or July onwards and has mauve flowers with buff stamens. Otherwise, late spring and summer flowering hybrids that might do (you can cut these down in mid Feb too, but you'll lose the early, larger flowers, and get more smaller ones later on) are Niobe (ruby red), The President (purply blue) and Xerxes (syn Elsa Spath) which is violet blue.

Guernsey Cream is an off-white colour that grows quite happily on a shady wall for me

If you want a yellow clematis that is extremely easy, I'd recommend clematis tangutica or any of the yellow ones which you can grow from seed, such as 'Radar'.

Goy members have over 800 pics of their Clematis on Goypeadia why dont you have a look and come back to us with some that you like?

Many thanks everyone. I'm pleased to find that you think a clematis will grow in that position. I had hoped there might be a suitable one but it seems there are many. I had not thought of a yellow or a cream one but will be considering those. I have looked up Victoria and Xerxes which would provide contrast. Thanks for your tip Heron and for the suggested website, Louise and I will look up clematis on Goypaedia. it looks as though I am spoilt for choice!