The only way I've found to deal with this on a non-jailbroken phone is to set the side switch to the non-silent setting, plug in headphones and then dock the phone. The chime sound will only play through the headphones and the phone will not vibrate.

EDIT:

This is a feature in iOS 6. You can schedule notification suppression by opening the Settings app > Notifications > Do not disturb.

Original Post:

Unfortunately, there is no native way to do that in iOS 5.

Like you thought, the notification center, currently does not allow customization in that way. I think Apple could have added features similar to that one, but have chosen not to, either because they haven't wanted to take the time (but that hasn't seemed to stop them in the past), or because they have a big focus on keeping things simple.