Cat with nasal discharge?

My cat has had green discharge from his left nostril for about 6 months now. I've taken him to the vet 3 times and he's been on 3 antibiotics, but it hasn't helped. Other than the discharge, he also coughs - sounds like he has a hairball but he doesn't actually throw up anything. Anyone have an idea what this could be? He's about 10 years old and otherwise in good health and eating well.