Clear out the room and spread drop cloths over the entire floor.
Place stools or ladders in the room and climb up to reach the ceiling. Place a stud finder against the stucco ceiling to find the rafters above. Mark the location of the rafters with a marker. Do this across the entire length and width of the ceiling to have visual fastening points for the covering.
Measure the square footage of the stucco ceiling. This is most easily done by measuring the floor's length and width, then multiplying the two measurements together.
Determine how many drywall panels you will need to cover the stucco ceiling. Since drywall comes in 4-foot by 8-foot sheets, if your stucco ceiling is 15-by-20-feet or 300 square feet, you would need 10 panels.
Measure and cut the drywall panels that will be used to fill the gaps using a tape measure, marker and drywall saw.
Hold the drywall sheets against the stucco ceiling and fasten them into the rafters using a screw gun and drywall screws.
Tape the joints between each adjoining drywall panel with drywall tape, then spread joint compound over the tape using a putty knife. Allow the compound to dry for three or more hours, then sand smooth with fine-grit sandpaper.
Pour primer into a paint tray and apply a coat of primer to the new ceiling with a roller. Let the primer dry for at least three hours, then apply the first coat of paint, using a color of your choice. Allow the second coat to dry, then apply another coat of paint to finish the job.