Preheat the oven to 350 degrees. Press the wonton wrappers into the bottom and up the sides of 12 cups of a mini muffin pan (make sure you leave the center open for the marshmallow). Spray the wontons with cooking spray.
Bake for 5 to 7 minutes, until the wontons just start to turn golden on the tips/points of the squares. Cool for 5 minutes (on the counter is fine). Keep the oven at 350 degrees.
Place a marshmallow in the center of each wonton cup and return the pan to the oven. Bake for 2 to 3 minutes, until the marshmallows soften and the wontons are golden brown.
Remove the pan from the oven and cool for 5 minutes. Keep the oven at 350 degrees.
Spread the coconut out on a dry baking sheet and bake for 2 to 3 minutes, until golden brown. Set aside.
Melt the chocolate in a small saucepan or in the microwave, checking and stirring every 20 seconds.
Use a fork to drizzle the chocolate over the marshmallows and wontons. Cool until set (this just takes a few minutes).