Preheat oven to 350 degrees F. Line a baking sheet with parchment paper and set aside.
Prepare cookie dough according to package instructions, stirring in the coconut as well.
Drop the dough in heaping tablespoons onto the prepared baking sheet.
Bake for 8-10 minutes, or until just golden brown on the edges, but still soft in the center.
Cool on the baking sheet for 2-3 minutes, and then transfer to a cooling rack.
Once cookies are completely cool, prepare the frosting.
In a small bowl, stir together the frosting, 1 tablespoon of milk, lime juice, rum, and lime zest. Add more milk, if necessary, until frosting reaches desired consistency.
Drizzle frosting over cooled cookies (I like to use a zip-top bag to pipe the frosting).