The most famous coconut cocktail is the piña colada, which is made with cream of coconut, pineapple juice and rum, typically blended with ice into a frozen drink. This coconut martini recipe, which its really a coconut cocktail served in a martini glass, is made with cream of coconut, vanilla vodka and coconut rum, shaken with ice. It's quite a bit stronger than a piña colada and is much more intensely coconut flavored.