Yeah, private islands are scattered all over the world. Though many can be bought, most are already developed as vacation rentals for wealthy persons.
Many islands can be rented out entirely as a vacation rental. Many such privately owned islands are fully owned by top celebrities. Such islands owners or developers usually seek the assistance of a highly reputed travel website to rent their property out and goin2travel.com falls in this category.
One can find several islands listed in goin2travel.com. Also, for your information, their San Diego vacation rentals are always in high demand mainly because it is home to miles of beaches and it boasts of a mild Mediterranean climate