We are hoping to replace carpeting in an upstairs bedroom with a laminate flooring. But the floor sags toward the center of the room. Can I still use a laminate or am I going to have to stick with carpeting?

First, do you have access to the joist below?

You can tackle the sag first with a product such as sag-ender: Quickly And Easily Eliminate Annoying Sub-floor Sags Or Seams, Sag-ender

You could also rip the ceiling out from below and fix the sag.

It probably makes more sense to fix the sag in the long run.