Carnival doesn't require it but "strongly recommends" it. Straight from the Carnival FAQ's:
Traveling with Minors
When traveling with a minor where one parent or both parents or legal guardians are not cruising, we strongly recommend bringing an original signed letter from the absent parent(s) or legal guardians authorizing the minor to travel with you. If there is no second parent with legal claims to the minor (due to sole custody, deceased, etc.) other relevant paperwork, such as a court decision, death certificate, birth certificate naming only one parent, would be useful to bring in place of a signed letter. This will expedite processing by the Department of Homeland Security.