If you are looking for a long term rentals you can check
www.jamaica-gleaner.com or
www.vmbs.com they have properties listed islandwide for long term rentals.
You are right my website is geared more towards short term rentals. You can also do as Princessblack suggests stay with someone for a week or 2 or rent somewhere for 2 weeks and then search as the local papers especially the Sunday Gleaner have all the properties listed. Its a really good source for finding anything for sale or rent in Jamaica.
Take care and all the best.