Remove the flesh from 1 brown coconut, reserving the water (see Cook's Note). Peel off the skin and cut the flesh into small pieces. Transfer to a blender and add the reserved coconut water; puree until almost smooth. Bring the coconut mixture and 1 1/2 cups water to a boil in a saucepan, then remove from the heat and let stand 30 minutes; strain through a fine-mesh sieve and chill. For each drink, shake 1/4 cup of the mixture with 1/3 cup pineapple juice and 2 tablespoons spiced rum in a shaker with ice. Strain into an ice-filled glass.
How to Reserve Coconut Water: 1. Poke the three eyes with a skewer to find the one that's soft. Push the skewer through the soft eye, working it in to create a 1/2-inch hole. 2. Drain the water, shaking the coconut to release all of the liquid. (You should get 1/2 to 3/4 cup coconut water.)
For a frozen version of this drink, blend the cocktail ingredients with 1 cup ice.