Heat oven to 350 degrees.
In a large bowl, combine all the dry ingredients (flour, sugar, baking soda, cinnamon, and salt).
In another bowl, combine the wet ingredients (eggs, applesauce, and vanilla).
Combine the dry and wet ingredients. Add in the carrots and coconut.
Spray muffin tin with cooking spray. Fill the cups with batter. Bake for 20 minutes.