I don't have any official numbers, but I can tell you this: I had the 470 which ran it fairly smoothly at 1080 and ran at 720 in 3D (in both cases on the highest graphics settings). I wouldn't go all the way to saying it was silky smooth (which I would say is a solid 60+ fps), but very smooth none-the-less (i.e. never really dipped below 30 fps).
I just recently purchased a 580 myself, since I also have no interest in overclocking or SLi. I haven't played C2 with it yet, but plan to this weekend. So I'll try to give you some info then (if I remember).
