I take one Bonnine ever 24 hours. That makes me drowsy too (so does Dramamine), so what I do is, start taking it about 2 days before my trip, so by the time I go, my system is used to it and causes no more side effects! Works like a charm.
I have noticed however that it does nothing for the dizziness that can sometimes happen after a ride on an upside down roller coaster. So I have to bide my time between rides.
Also, if I'm overly tired, I find I may need a second pill. Something about not getting enough sleep adds to the nausea problem.