The short answer to this is no. It's not possible to make up laws even if an island is private, simply because of the fact that it will already be governed by a country. Every piece of land in the world has been claimed and added to a country's jurisdiction, which means that choosing an island should also depend on the country the owner wouldn't mind being subject to. This means that the island in question would follow the same laws as set by the country which owns it, meaning no additional laws, rules, or guidelines can be set by the "owner" of the private island. [links]