If money is no object, you might consider Cayo Espanto. It's on a postage-stamp size island just to the west of Ambergris Caye. The resort has four deluxe villas, each with a splash pool, your own personal butler and all the modcons like cable TV, VCR and stereo. Meals are included and are served at your villa. Really nice, and really expensive (starting at around US$600 per night per couple, meals included.)
A bit less pricey is Mata Chica, on North Ambergris. Very stylish thatch cabanas, highly decorated. Good restaurant, upscale Italian and other dishes. No pool, but good swimming from the dock.
Both are quite romantic and offer privacy.
Belize First Magazine http://www.turq.com/belizefirst/