We own a vacation property in the Caribbean. We want to rent it to mature adults only because we have seen the destruction that students can do while on spring break, etc.

This is own home away from home and we wish to keep it nice. It is very difficult and very expensive to replace items such as mattresses, etc if we rent to families with children who might wet the beds, jump on them with wet bathing suits, etc. Also, there are no playgrounds or play equipment for children and the floors are constructed of very hard tiles that are common to the islands. Should a child fall and hit its head, the wound could be considerable and there's no close medical service. In other words, it is not suited for children.

Is it OK for us to advertise for "mature adults only"?

What country in the Caribbean ?

Yes, since this is vacation property that you are renting for short term, you can specify the type of people you want to rent to.