Add frozen pineapple (little at a time, depending on your blenders strength and capacity) and some pineapple juice (if using) and coconut milk to a high-speed blender. Then blend on high until creamy and smooth, using the tamper (if available) to push down and blend more easily. Add more coconut milk, as needed, to help blend easier and ensure creaminess.
Adjust flavors as needed; more coconut milk for creaminess, pineapple to thicken and add sweet-tart flavor, lime juice for more tartness, or a bit of agave syrup for sweetness.
Although already frozen, you may pour into large glasses filled with additional ice and top it with a cherry, a slice of pineapple, or mint.
Leftovers can be frozen into popsicles or ice cube molds (not if you’ve added rum). When ready to use, simply blend the piña colada ice cubes in your blender.
If you want the authentic cocktail taste add 1-2 oz of your favorite rum (white is preferred) and blend again to combine.