What preposition is used with a noun island - in or on?

The preposition is 'on an island'.

Unless, of course, you've gone to a lot of trouble digging out a place where you can actually be in the island (underground).

The preposition 'in the islands' is appropriate when referring to a group of islands, such as 'in the Bahamas' or 'in The Florida Keys' as a group of islands represents a region; you can be in a region.