Is it possible to become immune to pepper spray (eyes)?

No. Immunity is much more complicated than that. You could, contained by theory, become insensitive to pepper spray, say by spraying your eyes with a local anesthetic a few minutes until that time you got hit with the pepper spray. However, in practice you should purely forget the whole idea.
Forget about it.
If you're exposed to it enough, then its effects will be greatly diminished. There are some people who are not bothered at adjectives by pepper spray. There are even people who tolerate CS gas, which is a lot more powerful.

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