G.♣.
His eye does not have to be open in order to get the medicine into his eye. Seriously!!!
Have him lie down on the couch, close his eyes and relax. Put a couple of drops into the corner of his eye and just let it seep in. Even with his eyes closed, it really will seep in. Just have him lay there for a few minutes (5 maybe?) to give the medicine a chance to really seep in. After a few minutes, let him get up and go play (or whatever).
I understand why people say that taking medicine is not negotiable and to remember who the adult is, but that's so much easier said than done. It is completely normal for kids (and many adults) to freak out when it comes to something touching their eye. I know many, many adults who say they are so glad they never need to wear contacts because the very thought freaks them out!
Eye drops are a battle for many people, and it's just not necessary. Let him have the drops with his eyes closed. It works, so there's really no reason not to.