Preheat oven to 350 degrees.
Spray 9x5 loaf pan with a non-stick cooking spray.
In a medium bowl, add the eggs, milk, vanilla extract and lime zest. Mix to combine.
Using a stand-up mixer on low speed, combine the flour, coconut, sugar, baking powder, salt and cinnamon.
Continuing on low speed, pour in the egg mixture and mix until just combined.
Now add the butter and mix until combined.
Pour the batter into your loaf pan.
Bake for 60-75 minutes, or until a toothpick inserted into the center comes out clean.
Once the bread is cooled, make the lime glaze.
In a small bowl, whisk together the confectioners sugar and the lime juice.
Sprinkle with the lime zest.