Yes screen resolutions have been the designer's nemesis since the beginning. And now with all the mobile devices, it's a real mess.
Statistically, the 960 width should fit every modern monitor without much trouble. You're client may need to get a new monitor or adjust the resolution to see what most other people see. That's something most people don't understand.
Also the cool websites with the best display technology cost a lot more. Many of them in the 10's of thousands. I always found a client was satisfied with centering when they looked at the cost of perfection :)
Cheers,
Ed