So I have shopped for islands before.
There are some big ones available.
If we get one (an island) next to a fairly underdeveloped nation, and arm ourselves to the teeth, and offer some type of positive outcome for them like production of some kind or we could even beef up there technology sector and offer serious upgrades and expetise. Then they probably would rather allow us to operate then invade us.
But we have to make ourselves beneficial or we are going to war (or just failing all together).