Plant two and get the best of both. Climbers can look great growing into each other too. How about a good form of our native Woodbine for scent as one. A good clone could be either Lonicera peryclimenum 'Graham Thomas' or L. p. 'Sweet Sue'.

You could have with this an evergreen climber such as the so-called Star Jasmine (either species Trachelospermum jasminoides or T. asiaticum). They have white flowers, the second species flowers age to yellow and this one (T. asiaticum) is slightly hardier too.

I still think you can't beat a fragrant climbing rose, like Pierre de Ronsard or Madame Alfred Carriere. They can be rather rampant so you have to keep them in check, but you would get a pergola covered in scented flowers for much of the summer.
Take Fractal's advice and grow something else like a clematis or lonicera to intertwine with it though.

ps, forgot to mention that Star Jasmines have powerful scent also :-)

Bertie's suggestion for roses is of course another great option and if you are worried about thorns, Madame Alfred Carriere doesn't have too many (mostly on the first and lower part of the new growth). A good combination for this variety could be with a Clematis viticella variety. There are many but C. viticella 'Polish Spirit' is just about the longest flowering starting end of June and right through into late autumn once established.

If you're going to mix roses with other plants it can be a thorny job pruning, they intertwine so.What ever you choose it will be a lucky plant from your description of the site.