Choose a color that isn't so light that it will show dust or smoke, and complements your fireplace and room decor.
Clear everything from the mantel, and move furniture away from the area to give yourself plenty of space to work without spattering paint.
Clean the stucco to remove as much dust and grime as possible.
Repair hairline cracks with paintable silicone caulking. While the caulk is fresh, wipe it with a damp rag so it blends with the surrounding texture. Use stucco or masonry patch for larger cracks or chips. It's available in both pre-mixed and powdered form. Tile grout patch works well too. Follow the directions for drying times.
Protect the floor and adjacent surfaces. Use blue painter's tape to seal edges around the mantel. Tape some plastic, newspaper or masking paper to the surrounding wall for extra protection; you're more likely to spatter when rolling and brushing paint onto a rough surface like stucco. Use drop cloths on the floor.
Paint the edges and corners with a brush first, then roll the larger areas. Use a 1-inch nap lambswool roller cover if the stucco has a heavy texture. This will allow you to get into all the nooks and crannies effectively.
Apply at least two coats of paint. When the paint is dry, pull away the masking tape. Allow several days for the mantel to dry before putting anything on top of it.