They have a special offers. On our last cruise they had a margarita happy hour (2 for 1) in the Schooner Bar one afternoon, and I think there was another day they did something similar. Royal Caribbean doesn't tout it as much as Carnival does, but they do have a beer bucket deal. I think it is 5 beers for the price of 4.
They also have a drink of the day. Now, it was $6.25 on our last cruise but that was with the souvenir glass. I think you can order it in a regular (smaller) glass and the price is cheaper than a normal cocktail.