If your ceiling drywall is sagging between joists, sometimes called “pillowing,” it's probably on the top floor and attached to the roof trusses. If so, I bet the installers used 1/2-in. drywall instead of 5/8-in. Half-inch drywall can sag if it’s hung under roof trusses that are spaced every 24 in. It isn’t strong enough to handle the span, and the weight of the attic insulation just makes the sagging worse.
You only have two choices: Rip it out and replace it with 5/8-in. drywall or add spacers and new 5/8-in. drywall below it. Ripping out the old stuff is the most professional approach, but it's a nightmare job. You have to pry out the ceiling drywall along the edges and pluck out all the old drywall screws. As if that weren’t enough fun, the attic insulation may collapse into the room.
If you can live with a lower ceiling height, you can save a lot of time by installing a new ceiling below the old one. Add the 1-by furring strips (on 16-in. centers) shown in Figure A. Use 1x3s rather than 1x2s because it makes the drywall easier to hang. (But if your ceiling sags more than 3/4 in., use 2x2s.) Screw the 1x3s to the truss framing with 2-1/2-in. drywall screws spaced every 2 ft. Next, install and tape and finish new 5/8-in. drywall. If you have ceiling fixtures, you'll have to extend all the boxes so they're flush with the new ceiling.