There were signs at the port last week that said 'no weapons and no alcohol', but I didn't have any trouble. My wife and I guessed it was referring to open bottles/containers. I had liquor in my carry-on and it went through the machine just fine. I wouldn't worry.
I also bought liquor in Nassau and brought it back on the ship without problems.
The only issues I had was with duty free. I bought a bottle and was told it would be delivered the last night. It never showed up. I was told that was because we had the 'privacy' sign out. You think they'd leave a note or something, or the CM would let me know not to put the 'privacy' sign out.
Anyway, I spent an hour tracking down the $10 bottle and having it delivered to guest services the last morning. Won't be doing that again, but Nassau Royale is kind of fun to have at home.