What's the best way to ask my boss to reconsider the schedule?

I work at a casino, so our department is open 24/7. There has been a lot of friction between the cashiers because the schedule is horrible and unorganized. Some people think we have too many people, other people think their days off are unfair, and then there's me... having to work six days a week whenever someone quits or goes on vacation... while NO ONE ELSE has to work overtime. (In the month of August, I had four scheduled days off... I actually took six because I had a family emergency and had to leave the state.) I think the best way to try to rectify the situation is to completely re-do the schedule. I have a couple of ideas. But how do I present this to my manager without getting into trouble? It's something that seriously needs to be looked at and I can't handle the arguments it causes anymore!