This is kind of strange, but I found the Children's Bonine at The Christmas Tree Shoppe. I don't know if they have those by you. It's sort of discount everything for the home store (not just for Christmas stuff). They have a huge section of travel size stuff and they sold both Children's Bonine and the adult version.
I decided not to give it to my kids unless I thought they needed it. They were fine the whole cruise, even with really rough weather on some nights. The last night though, my DD got really sick so we gave her one and she was better quickly, though not sure if that was the work of the Bonine or just that she herself was just done being sick. DS was not sick at all, but we were going to use Benadryl for him if needed since he was only 3 at the time and we had already use Benadryl previously for his allergies.