Ahh no. Even buying an uninhabited island from a country wouldn't work since no one would sell it to you and secondly, almost every island in this world is already under the sovereignty of a country
An alternative would be to buy a whole existing nation. There are several struggling Pacific microstates that are threatened with inundation by AGW and whose inhabitants already have the right of abode in another country. The idea would be to wait until most of the inhabitants had left, then offer the remaining ones $$$ to (a) amend their constitution to make NewCountry Inc. the sovereign, and (b) leave.