Chill a clean ice cube tray in the freezer. For the cheesecake filling: In a food processor, mix together the cream cheese, yogurt, confectioners' sugar and vanilla until smooth. Pour into a large resealable plastic bag and set aside. Clean out the food processor bowl for the chocolate covering.
For the chocolate covering: In a food processor, mix together the cocoa powder, coconut oil and confectioners' sugar until smooth.
Using a pastry brush, grease the chilled ice cube tray with coconut oil. Spoon the chocolate shell mixture into each compartment, tilting the tray around to coat the sides. Cut a small corner off the bottom of the bag of filling and squeeze into each chocolate mold. Spoon more chocolate over the filling to cover. Freeze for 4 to 5 hours, or overnight.
Before removing the cheesecakes, set the frozen tray on the counter for 2 to 3 minutes to start defrosting. Remove as you would ice cubes, by twisting the tray, or running the underside of the tray under warm water for a few seconds. Serve immediately.