You should use some sort of artists' sculpting tool or dental instrument to get into the recesses and scrape any loose and peeling paint.
You will then probably want to use an artists' brush to lay down a coat of bonding primer. Finally, finish with sign painters paint in the color of choice. You could jump right to the sign paint but the job will not last as long as it will if you prime under it.
Your art store should have 1-Shot which is an alkyd paint and tried and true fave of sign painters and pin-stripers because it goes on evenly and does not "crawl". It comes in many colors and they mix well together to make anything you have in mind. The great news is you can buy it in cans as small as 1/2 pint. You will not need a lot.
You will need paint thinner or mineral spirits to clean your brush.
Last edited by user1007; 04-20-2013 at 06:44 PM.
Reason: Added Image
Power wash off the grime, after presoaking with Tide detergent, then use TSP to further scrub with a brush, rinse off, and let dry. After drying, use something like Rust-Oleum to paint the numbers. If they just painted the numbers on top of the stone, you will need stencils, so that they look professional. Otherwise, if they have been routed out at a stone shop, then just keep inside the lines.
You could use two colors, one for the side inside the routed number, one for the face. After done, then let dry, and if you wish, use a Poly coat to protect the paint, which should allow it to last a very long time.