I got one called Supergoop because I saw it recommended for runners somewhere, and it did seem mostly eye-burn-free, but today towards the end of my run, my eyes started burning again because the dripping sweat current from my forehead was transporting the sunscreen into the corners of my eyes.
A hat
Coppertone Sport
Banana Boat Sport, SPF 50. I run before sunup 90+ percent of the time, but the rest of the time, I use this sunscreen every time. It doesn't irritate my eyes, even when I get seriously sweaty. At almost 50 years old, I've had no dermatology ssues.
I've had absolutely no luck finding a sunscreen, but when I have to do a mid-afternoon run I've started carrying a mini-towel-type cloth that we had around from when my baby was younger. I think they're called burp cloths or something like that, but they're easy to run with and do a much better job wiping than my sweaty, sunscreeny hands lol.
I use cerave 30 spf AM cream. I also have heard good things about Korean sunscreens as they're light and very protective
Neutrogena mineral sunscreen for babies doesn't sting my eyes.
I’ve had no eye problems with Kineysis, but I have not had a super sweaty run yet this year.
For me - the stick sunscreens (the packaging looks like deodorant). Neutrogena and Shiseido are the brands I use, but I'm sure there are others.