I would first check with your auto insurance back in Puerto Rico to see they would cover you and the rental car you are using here in the U.S. If you are using a major credit card to rent the car, it might also allow you full coverage through it.

If neither your Puerto Rican auto insurance or credit card cover your rental car in the means that you need many insurance companies will allow you to obtain insurance with your Puerto Rican driver's license since it is a U.S. Territory.

Unfortunately many insurance companies do not like to write policies for less than 6 months so if you need to purchase insurance in this manner you might have to buy a 6 month policy and cancel it when it is no longer needed. Also it may be difficult to get full coverage on a rental car since you will have to obtain non-owners insurance.

Foreign Travel Insurance Protection is a news article you might find of interest.