The place your looking for is Serenade Island Resort www.belizecayes.com
HapiHapi posted a report from their trip there just a few weeks ago...You will find it on this board.
It is a 4.5 acre private island with a total of 3 Cabanas ans a staff of about 6 people.
The caye sits directly on top of the barrier reef in the southern end of the reef called the Sapodilla Range.
They also have an onsite dive shop, canoes, kayaks, deep sea fishing, snorkeling, camping etc.
They provide all meals as there is no place else to eat.
Most times you would have the caye completely to yourself except staff.
The also have a guest house in Placencia, Serende Guest House, which is the jumping off spot for the trip to the caye.
Lance and Veronique McKenzie would be your hosts.
We have been there a few times and can't wait to go back....best time is Nov ~ May.