To separate the coconut solids in your coconut milk: Put a can of coconut milk in the fridge overnight. When you're ready to use it, open it (without shaking it), and scoop the solid part out. (For this recipe, it's ok if you get some of the watery part). Save the rest of the coconut water for a later use.
After you've stored your frozen yogurt in the freezer overnight, it'll harden more than normal ice cream (because there aren't stabilizers in this recipe), just let it sit out to thaw for 20 or so minutes and it'll become creamy again.
Vegan option: skip the yogurt and use 2 (total) cans of full fat coconut milk instead.
I have this Cuisinart ice cream maker