Although the official policy is technically against it, you can probably bring a case of bottled water on board with you. If you choose to do that, slap a Royal luggage tag on it, put it in one of those canvas-like grocery bags and tie the handles together. (They don't mind handling luggage with handles; without you're much less likely to get it delivered to your stateroom). Worst case you're out the cost of a case of water. (Many do this...And I would not recommend trying this with anything but water)
The policy has changed! As long as you carry it on yourself you can bring on your own non-alcoholic drinks:
"Royal Caribbean now allowing guests to bring non-alcoholic beverages onboard.
Royal Caribbean has updated its non-alcoholic
beverage policy for guests, beginning on September 1st, 2018.
Guests bringing small quantities of non-alcoholic beverages onboard are now required to do so in a carry-on or hand luggage, rather than in a checked bag.
The cruise line announced that guests will be able to bring small quantities of non-alcoholic beverages in a carry-on or hand luggage onboard only on boarding day. Checking in non-alcoholic beverages will no longer be permitted.
Specifically, non-alcoholic beverages brought onboard may not exceed 12 standard (17 oz) cans, bottles or cartons per stateroom. Distilled water or specialized beverages such as, milk for medical purposes, dietary or infant use, are permitted.
Guests are prohibited from bringing alcoholic beverages onboard any cruise ship, with the exception of
being able to bring two bottles of wine per stateroom."