To see a how bad the sag is put a nail 1" up on the side @ both ends of the suspect lumber from where the ceiling would be attached. Then run a string from nail to nail pulling it tightly. This should show you where the sag starts and ends( if less than 24" see paragraph below), and how bad the sag is.
What about putting 1" x 3" furring strips 24"oc going the opposite direction of the existing joists. Configure the furring strips so that the space between the stips goes where the sag is. Then 5/8" drywall for your ceiling.