The non-confrontational approach is to simply ignore him and let the quality of your work speak for you. Like the others have suggested, try advertising via flyers that contain testimonials.

However, please be aware that his spoken statements might be legally actionable. It sounds like you might have a case for "defamation of character". Simply put, defamation of character is spoken or written words that falsely and negatively reflect on a living person's reputation. If a person says something about you that is understood to lower your reputation, or that keeps people from associating with you, defamation has occurred (slander is spoken, libel is written). In order to prove defamation, you have to be able to prove that what was said or written about you was false. You may also bring a defamatory action if the comments are so reprehensible and false that they effect your reputation in the community or cast aspersions on you.

Doing all this is a hassle, as you have to collect witness statements and waste your time meeting with attorneys and go to court for God-knows how many times and how long. However, if this is affecting your livelyhood, it just might be worth it.

You might want to talk to this guy in a calm manner, and explain to him that you don't care if he doesn't like you, and you don't know and don't care what kind of beef he has with you, but because his false statements are affecting your reputation and your livelyhood, you will consult an attorney if he does not stop.