I have motion sickness on land quite often due to an inner ear problem and I've been on a cruise to the Caribbean in both directions. The Eastern cruise was on the Magic and the western was with Carnival in early 2001.
The Disney ships seem to have very good stabilizers and you don't feel much motion with them
I have a Prescription for Antivert (generic name is Meclizine) and I take one tablet 30 to 60 minutes before getting onboard, about 12:30. My Rx says I can take it as often as once every 4 hours and I take a second one by 5pm when we pull out.
On the first evening at sea, you pass over the Gulf Stream as you head south, and the ocean tends to be more turbulent. This can be as early as 6pm and it is usually over by 10 to 11pm. Sometimes I need a third tablet by bedtime but not always.
I also take 2 capsules of Ginger Root, an herbal supplement, every morning and every evening for at least two weeks before I'm going to cruise, and also during the cruise and for a couple fo days after I'm home. It is known to help with motion sickness and queasy stomachs and has very few side effects.
After the first evening at sea, I use the Prescription only as needed, and it usually isn't even once per day.
On our cruise on the Magic in January to the Eastern Caribbean, I needed the Rx on our shore excursions instead of onboard. We were on the See and Sea and the boat ride to the reef was a little choppy. We had an Island Tour at St Thomas and the driver took the turns on the winding road with a little too much enthusiasm, but I made it.
One thing that does seem to bother me is if the ship is travelling at cruising speed of 21 or 22 knots and I'm walking on deck 3 from the stern towards the bow and I look out of the huge portholes near Promenades Lounge or Lumiere's. It seems to exagerate the motion and it bothers me a lot after dark.
I tried an inexpensive pair of the wrist bands and didn't notice much relief with them. I haven't tried the patch behind the ear.
Many others have used the Over the Counter product called Bonine with much success. It can be purchased in a chewable tablet form that you take once per day. They also have Bonine tablets available on the ship when the waters are rougher than usual.
Anything that you try for motion sickness should be tried at least one week before the cruise to make sure you can tolerate it without side effects.
Even with my inner ear problem, I enjoy cruising very much. We've been on 4
DCL cruises and we have two more booked, and we've been on 1 cruise with Carnival.
I'd say it is definetely something that is doable.