If you have painted the neighbor's side of a wood fence can the neighbor make you replace it with a new wood fence?

Perhaps you have mixed up your words in your question. It makes sense if read as, "If you painted your side of your neighbor's wood fence can the neighbor make you replace it with a new wood fence?" If that is the case, you had no right to paint your neighbor's fence without their permission and the answer to your question is they can sue you in court for damaging their property.

If they sue you in court and prevail, they have the right to be restored to the position they were in before you damaged their property. If the fence is new the court may award enough damages to cover a new fence. If the fence is older, the court may pro-rate the value. While your neighbor cannot make you replace the fence, the court can and you may have the added burden of legal expenses. You should try to negotiate a friendly agreement to resolve the issue either by repainting the fence to please your neighbor or perhaps offering to share the cost of a new fence.