My cat has gunk in his eyes all the time?

I have an 11 yr old Maine Coon male, he does in fact have a bit of asthma, vet confirmed, wheezes, snuffles etc. But not when asleep, he is fine then. But he exudes a gunk from his eyes too, the right one more than the other, sometimes dark, sometimes yellowy stuff, then he sometimes sems to exude more liquid, i suspect a reaction to wash it away, which leaves him a mark of wetness from the corner of his eye down the side of his nose. I clean it every day, but he objects, and scrunches his eyes tight shut, naturally enough. I can see what I think is causing the irritation, as there is sometimes a deposit of black harder gunk on his bottom eyelid, but there is no way i can dislodge it, anyway i would rather treat it so it didn't happen in the first place. Is there something commercially available I can give him, either to the eye, (should be an interesting reaction from the puss in question!!) better "suit up" Or is there something I can give him to take with his food for instance.