There is a website that is offered by some agents who work for Sudler Sotheby's International Realty that specializes in rentals. It is:
I have not yet used the website, but I know that it is not limited to rental listings that are found in the Multiple Listing Service which most Realtors use. It might a rental that fits what you're looking for. Good luck.
Broker Associate, Sudler Sotheby's International Realty