Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper or Silpat liners.
Whisk flour, coconut (don’t forget to finely chop it!), baking powder, baking soda, and salt together in a large bowl.
In a medium bowl, place 1 1/2 cups sugar, lime zest, and cream cheese. Put the other 1/3 cup sugar in another bowl for rolling, and set aside. Pour warm butter over sugar and cream cheese and stir to combine. Stir in oil, then egg. Add milk and lime juice and continue to stir until smooth. Combine with flour mixture and mix until a soft dough forms. Refrigerate dough for 15 minutes.
Portion dough into small rounds about the size of a golf ball or approximately 1 1/2 Tbsp. I usually fit 12 per baking sheet, but these can spread a lot so I would recommend trying 9 at first so that they don’t all run into each other. Roll each ball into the reserved sugar and return to the baking sheet. Flatten slightly with the palm of your hand. Work quickly as the dough can become warm which can cause the cookies to flatten too much when baking. Bake 11-13 minutes, or until edges are set and just begin to brown. Cool on baking sheets for 5 minutes before transferring them to a wire rack to finish cooling. Store in airtight container.