Cocktails could conceivably be patentable, if they were sufficiently novel and non-obvious, which very few cocktails are likely to be.
If you used a sufficiently visually distinctive glass and created a fanciful name, you might be eligible for trademark protection -- that wouldn't stop someone making the same cocktail, but would prevent them using your identical glassware and name in a way that might lead to confusion that the cocktail was approved by you.
Oh! And if you choreographed an interesting process of making the drink, with a specific sequence of unnecessary but distinctive motions (think "bartender dance"), you could copyright your performances of the dance act and possibly prevent others from stealing your show. The less elaborate your performance, the less protection you're likely to get, and copyright doesn't prevent, for example, parody.
But generally, intellectual property rights are not intended to vest in ordinary creations like mixed drinks.