Check with your local art museum. Many art museums offer classes for children, and some maintain separate children's galleries. Search online by museum type or by location. Once you find a museum, visit its website or call and ask about children's programs.
Consider your local YMCA. Many YMCAs offer children's art programs regularly, in sessions that last a few weeks long, for reasonable prices that are reduced if you become a member of your local Y.
Look into art camp. If your child is really enamored with art, you may want to immerse him in an intensive program of art classes. Whether you choose day or overnight camp, your child is sure to benefit from exploring the arts in ways that school cannot provide.