First of all, I hope that you have a wonderful cruise and for most people sea sickness is not an issue. My advice would be to buy bonine before leaving home. Take one bonine pill every night before you go to bed, and to take your first pill the night BEFORE you get on the cruise. Even though it is not suppose to cause drowsiness it can cause you to feel a little different. That is why I suggest taking it before bed, because if there are any effects it is while you are asleep.
If you feel like you are doing okay stop taking the pills and see what happens. If you start to feel bad during the day take an additional pill, order a ginger ale, and get on deck where there is fresh air, but do NOT sit near the edge were you can see the horizon bobbing (if it is bobbing at all).
Oh, if you are into a more home remedy solution start taking ginger pills two days before boarding the ship once a day and take ginger pills twice a day while on the ship. I personally do not think this works as well, but others swear by it.
Oh, a side note to everyone, the front desk will give you packets of bonine for free if you ask. Each packet contains two pills. If you are feeling sick go straight to the desk and ask for the pills. Read the directions on the packet, take the recommended dosage, get a ginger ale, and get in the fresh air! Lastly, do not sit in the hot Caribbean sun if you are feeling sick. Find a breezy, cool, shady spot where you are not looking at the bobbing horizon.
That is my advice take it for what it is worth.