The winter months -- especially during the Christmas holiday season, from late December through the first week of January -- are the most popular times to visit Hawaii. This is the best time of the year for whale-watching (whale season is November through early May), but it's also when the weather is the rainiest and flights are most expensive. Summer is a popular time for family travel, though only Norwegian is offering cruises at that time.
Shoulder season would be May through June and September through mid-December. The weeks between Thanksgiving and mid-December are an especially good time for deals. Late-spring sailings tend to offer great weather and less-crowded ships (since kids are in school). April, September and October can also see a larger selection of cruise ships visiting the islands, as ships tack on Hawaii cruises as they reposition between Alaska and their winter-season homeports.