State Farm may be one of the few that do cover, not sure. Seems to be the case, but read your policy to see if it specifically cover US Territories or not. Also read it about the type of vehicle that is covered. Some do not cover jeeps for example, which would be a typical rental in St. John.
Some Visa/Mastercards also include coverage so check with your cards also. They might cover any deductible you would have under your home policy. Some cards also have "primary" coverage vs "secondary" coverage. That makes a difference also. Primary coverage is when the CC covers the cost up front for the rental, you do not even contact your home insurance carrier.