Hi louise, i agree with what terry says, i did it in july of this year and stayed in quite a lot of pensions and hotels along the coast, i was keeping an eye when they were open out of season, because i was thinking of coming back with some mates and doing a spot of fishing, and all seemed to be fine up to the end of october.Another member(Caminitoito) has posted a link to a list of albergues, and you can click on indvidual ones and they give you the dates they are open(the ones i checked will be fine for you) his post was dated 25/oct/09 (on this norte topics page).
I dont think september will be all that quiet, that was my other option for a month(August would be packed with the spanish on their month long holidays) and i feel from what was being said to me by other people that if they hadnt done it in july then september would have been their choice.
Good luck and Buen Camino