I can't tell you how many times I've gone through this fight with my kids, LOL! We just had pinkeye again a couple weeks ago. One peice of advice -- hold onto those drops b/c they don't expire for over a year, and they may come in handy again later.
One thing I found that helped a TINY bit with my daughter was letting her take the drops herself (with the top screwed on) and "put the drops in" her teddy's/dolly's/whomever's eyes. I had to fight with her to get them in at first (she's 18 mos, and very opinionated, LOL) but once I let her have "control" of the drops and "use" them herself on her toys, she became less defiant about it. I'm not going to lie -- I still had to hold her down and struggle, but it wasn't NEAR the kicking and screaming we went through before.
Every kid is different, but I figure it's worth a try! With my son (2.5 years) after I put them in his eyes last time, I asked if it hurt. He said no, it tickled. So after that I would say "Mommy needs to tickle your eyes again!" when we went to put the drops in. For some odd reason that worked for him. That, and me letting him "put drops" (again -- closed top) in his stuffed Dora's eyes.
Good luck!