Although other major cruise lines have their own private islands - RCCL, NCL, Princess and HAL, the largest cruise line, Carnival does not.  That may change.  Recently Carnival petitioned the Bahamian government for permission to build a private island on Eastern Grand Bahama.  This island is one of the largest of the islands in the Bahamas and also the closest to the U.S.  It is too early at this time to know if it will be approved, but the news is exciting.  Freeport is not popular with passengers, many of whom do not get off the ship when it calls here.  See the link below for more information.

http://cruisefever.net/08251-carnival-cruise-line-looking-to-add-private-port-in-the-bahamas/