Remove the light fixture with a screwdriver, and tape over the electrical box beneath with masking tape.
Sand off the old finish with a pole sander, fitted with a medium-grit sanding pad. Sand in the direction of the wood grain.
Sand with a foam sanding block around the edges of the ceiling and in any spots you can't reach with the pole sander.
Apply wide painter's tape along the top edge of the walls to protect against overspray.
Fill a clean bucket with paint and insert the end of the hose that connects to a pump-type paint sprayer. You can't use a container-type sprayer to spray a ceiling because the angle of the sprayer will not draw paint into the spray gun.
Practice painting on a scrap of wood before spraying the ceiling. Adjust the nozzle of the sprayer to a fine, light mist.
Spray the ceiling, starting in one corner and applying the paint in a thin coat, using uniform, side-to-side arm movements. Cover the entire wood ceiling with one coat of paint. It's OK if the wood shows through. Let the first coat dry completely.
Apply a second thin coat. It may take multiple thin coats of spray paint before you achieve the desired result.
Remove the painter's tape along the walls and reinstall the ceiling light after the painting is complete.