Follow BobCats advice and use Gobeach, a local on island business.

This VRBO business seems to keep changing their terms for owners and renters. I did find a nice condo in Hawaii 3 years ago, but the owner said to deal directly with him and all went well. Since the changes, his condo isn't listed.

http://www.gobeach.com/sxm.htm will show you many villas for rent.