I don't believe there is a limit as to how much alcohol you bring on board. On our previous 3 cruises, we have taken 12 beer, 4-5 bottles of wine and bottled water. They request that it is in a carry on. We generally have the beer in a paper bag and put the wine in a napsack. Even the kids help us carry it onboard.
If you bring wine to dinner, they charge you a corkage fee. We have always purchased the wine package and find this a very worthwhile way to have wine with dinner.