Press a piece of newspaper onto the face of the clock. Trace the outline of the clock's face onto the newspaper. Remove the newspaper from the clock.
Cut around the tracing on the newspaper with a pair of scissors. Cut as precisely as possible.
Place the cut newspaper back on the clock's face, and place tape around the edges . The tape should follow the round lines of the clock's face and not touch any of the black areas that you plan on repainting.
Spray a soft, lint-free cloth with a mild cleanser and wipe down the clock. Sand the clock with a 100-grit sanding block. Repeat with 220-grit and 360 grit sanding blocks.
Wipe down the clock gently with a tack cloth. Hold a can of oil-based primer 6 inches from it, and spray it with a light coat of primer. Allow the primer to dry overnight.
Hold a can of oil-based paint in the shade of your choice 6 to 8 inches away from the clock. Spray the clock with a light coat of paint. Allow the paint to dry for 24 hours, and then spray a second coat of paint.
Remove the tape and newspaper from the clock's face very carefully as the second coat of paint dries.