Costa Cruises' CostaRiviera, the former Marconi, currently being rebuilt by the Mariotti Company at the Genoa Shipyards, will sail her inaugural cruise from Port Everglades to St. Thomas, St. Croix and Nassau on December 14, 1985, and repeat this itinerary thereafter, according to the line. CostaRiviera will sail under Italian flag with an Italian crew.

The 31,500-ton, 984-passenger ship is being refurbished for $38 million, and will have new facilities, cabins, decks and hallways when she sails, spokesmen for the line reported.

Rates for the seven-day sailings are $965-1645 per person, double occupancy, with free air available from more than 100 U.S. cities.