While I do think that it may be too late to book for a long term rental in February there are still some bargain places to find on the island. Just to think of a few off the top of my head there is Heredia House Rental which goes for a pretty good price. This place is for the more budget traveller. If I am corret there is number is 501-226-0132. There is also the apartment at Rainbow Hotel which is located on the beach. There number is 501-226-0123 and if you contact them at [email protected]
they would be more than happy to send you an information packet.