Preheat oven to 350 degrees and lightly spray the donut pans with cooking spray.
Squeeze the zucchini shreds between a paper towel to remove excess moisture.
In a medium bowl, combine flour, cocoa powder, baking powder, salt, and baking soda.
In a larger bowl, lightly beat the eggs, and then add the coconut sugar, brown sugar, Greek yogurt, applesauce, vanilla extract and zucchini.
Mix the dry ingredients into the wet ingredient, and stir until well combined.
Spoon the batter into the donut pan, and top each donut with 8-10 chocolate chips.
Bake for approximately 9-11 minutes until a toothpick inserted into the center comes out clean.
Allow donuts to cool on a wire rack, and drizzle with glaze (combine 1/4 cup of confectioners sugar with a dash of milk and vanilla extract) if desired.