Villa du Soleil is amazing but this and Rainbow Tree are not in Negril, but in Treasure Beach...about 1-1/2 hrs from Negril. Treasure Beach is great but very different from Negril and not the same white powdery beaches.

I am not sure if this place is still available as a rental or not Bnewb probably will know.
http://hatihatijamaica.com/index.html

There are not really a lotof (if any) stand alone villa rentals on the beach.

The owners villa at Nirvana may fit your needs:

http://www.nirvananegril.com