If you have legal guardianship of your son, it should not be a problem. But I would highly suggest you bring the legal documentation with you proving you have sole custody. If you have joint custody or there is not legal documentation, it can be a problem.
This is directly from Carnival's website;
When traveling with a minor and both parents/legal guardians are not cruising, we strongly recommend bringing an original signed letter from the absent parent/legal guardian authorizing the minor to travel with you. This will expedite processing by the Department of Homeland Security. Please note that a notarized letter to this effect is required if debarking with children in Mexico.
In a situation like this, it's better to have it and not need it, than to need it and not have it.
Hope this helps.