Preheat the oven to 400 degrees. Line muffin tins with paper liners or grease. Set aside.
In a small bowl, whisk together the cream cheese, granulated sugar, and vanilla extract until smooth. Set aside.
In the bowl of a stand mixer, beat the eggs, water, oil, and vanilla together until smooth. Add the flour, both sugars, baking powder, soda, spices, and salt, and stir until just barely combined. Quickly fold in the carrots and coconut.
Fill the muffin tins 1/3 full with batter, then divide the cream cheese filling between the muffins cups (try to keep it from touching the sides of the muffin tins. Then put an additional scoop of batter on top of the filling to cover the cream cheese. Tins should be about 3/4s full.
Sprinkle with coarse sugar and bake for 22-25 minutes, until the tops are browned and spring back when you press gently on the top.