I have two really nice condo units for sale that might work for you. See details at: www.ambergriscaye.com/paradisevillas/sale.html
Cash only, no "seller financing."
As far as living aboard a boat is concerned, I am sure that there are many people with docks who would be willing to rent you dock space at a reasonable rate, don't know how many have electrical hookups, so you would probably want a generator. I think maybe the Paradise Hotel rents space on its dock.
There are no real marinas on Ambergris Caye. The Yacht Club claims to have a marina, but it does not offer any services and the rents are seriously overpriced. (At least they didn't offer any services as of last summer, maybe that's changed by now....)
The big problem with bringing in a boat nice enough to live aboard is the government of Belize. The import duties on boats is very very high, I think its around 75% - and they base their valuation on anything they want (not necessarily what you paid for the boat). The only way to get around that is to be granted "qualified retired person" status. You can find out about that on the net, by going to the Belize Tourist Board web site. I am not sure how long you can have your boat in Belize under visitor status before they start to hit you up for import duties. Cruising sailors come to Belize all the time and stay for a few weeks, so for short periods of time its not an issue.