IIRC they also sell "Dramamine less drowsy", which is the Dramamine with meclizine, on the ship. And as another poster said, they have two-packs of a generic meclizine available by the health centre -- note that they are chewables and contain aspartame, if that is an issue for you.
In the US, in most airports I have been in, you can find "Dramamine Less Drowsy" [it comes in a tube of 8 pale yellow tablets] in the "newstand"-type type stores that sell personal care and OTC meds [eg travel size packs of Tylenol, shampoo etc]. It seems to be one of the items that even if the store has just a few of that type of item, they will often have it. A bigger selection and it is almost guaranteed they will. This is what you are looking for:
http://www.dramamine.com/motion-sickness-medicine/dramamine-less-drowsy
Meclizine is no longer being manufactured for sale in Canada and is no longer available in Canada under any brand or generic names, neither Rx nor OTC.
For my motion sickness on the cruise, I take a combo of Dramamine Less Drowsy, Gravol/Dramamine "natural" ginger tablets/capsules, wear SeaBands, and drink ginger ale/eat gingersnaps. For me it does not entirely get rid of the issue, but makes it tolerable. For some reason my last cruise (#5) I barely noticed the remaining symptoms most of the time, while on our previous cruises it was noticeable all the time. I have the original Gravol as a backup if needed.
SW