Mildew

Black, gray, green, or brown spots on any surface. Paint does not cause mildew.

Mildew forms interior and exterior surfaces that tend to be damp or receive little or no direct sunlight.
Painting over a substrate (e.g. the surface that was painted) containing mildew.

Test for mildew by applying a few drops of household bleach to the area, if it is bleached away, the discoloration is probably mildew; if it does not disappear, it is probably dirt.
Before painting, remove mildew by washing the surface with a solution of 1 part liquid bleach and 3 parts water. Apply the solution and scrub the mildewed area. Allow the solution to remain on the surface for 10 minutes. Rinse thoroughly with water and allow the surface to dry before painting. Wear protective eyewear, protective clothing, and waterproof gloves. Quickly wash off any of the mixture that comes in contact with your skin. Do not add detergents or ammonia to the bleach/water solution.
To protect against mildew, use a top-quality paint, and clean when necessary. Install an exhaust fan in high-moisture areas.
Use a product that contains agents that inhibit the growth of mildew on the surface of paint film.
If mildew is the only problem, painting may not be necessary after cleaning the surface.