While it is good to have one, as long as you are a parent, it is not required from my experience. We always travel with my stepson, and so I called
DCL regarding this topic (my husband does not have custody). I asked if anything was needed, and they said no, as long as a parent was traveling with him, it is only needed if a minor is travelling without any parent at all.
In fact, I was the one who checked him in while my husband was returning the car, and even with a birth certificate with his real mother's name, not mine, they never even questioned it! I also was the one who went with him to immigration in St. Thomas, again husband was absent, (see a pattern here? ha ha), no problems then either.
As long as your name is on the birth certificate, there shouldn't be a problem, IMHO.
Have a great cruise!