If it's a matter of buying or leasing (under the condition of total autonomy for X years) an island from an existing government, there should be plenty of more willing governments here in the Western Hemisphere. Australia is a rich nanny state, while many countries in the Caribbean could use the money.
I think you mean, many countries in the Caribbean are flipping through another decade-long installment of Publishers Clearinghouse rule, before their leaders seek asylum in Europe.
You can buy land for a billion dollars, and the next government may invalidate the purchase.
What you have to buy is a piece of the government, not the land. The land is a commodity, and has value. But it doesn't grant you any rights.