What to do if my homeowners insurance won't cover a damage caused by my son due to his age?

That is not quite true. You could potentially be liable if you failed to monitor or supervise him properly--that is, it's not your son who was necessarily at fault, it may be you. For example, if you let your 4 year old outside without someone monitoring him, that could be held to be negligent. If your neighbor sues you, there is a reasonable chance therefore that you'd be liable for the cost to repair and repaint.

You could potentially then sue your insurer to force them to honor their policy obligations (check the policy to see to what extent they are obligated in a situation like this).