Preheat oven to 350° F.
Grease a 9x9-inch baking tin and line with parchment paper, leaving some overhang so you can lift the bars out.
In a medium mixing bowl, whisk together the melted butter, sugar and brown sugar.
Mix in one egg until fully combined, then mix in the second egg, vanilla, baking powder, baking soda and salt.
Fold in the coconut and flour.
Spread the dough evenly in the tin and bake for about 28 minutes.
Let the bars cool in their tin for 5 minutes, then remove from the tin and allow to cool completely on the wire rack.
Using a hand mixer or stand mixer on medium-low speed, beat together the cream cheese, lime juice, lime zest, vanilla and salt until smooth and creamy. Do not over-mix.
Spread the cream cheese frosting over the cooled bars, then top with more lime zest, if desired.
You can eat the bars right away but they are better if you let them chill and set in the refrigerator for an hour or more.