hmm probably Coventrians? all the other alternatives just don't sound right lol. I mean you could also go for Coveners for short, but that gives off a more witchy vibe, which my island is not.
My island is called Cherry Bay, so I guess I would call a single villager "cherry" or "Cherry Bayer" and all villager together "the cherries" (I'm not really creative...).
Lunarians from Lunaria! I almost didn't name my island Lunaria because Lunarian is used in a lot of other contexts (most fictional), but usually for the same thing (moon inhabitants), so I didn't let that stop me in the end. I'm pretty serious about RPing my island's context with letters, design etc. (although I've been lax lately), so it was important to consider this aspect.