Preheat oven to 350 degrees. Butter a 9-inch square baking pan. Line with parchment paper or foil, leaving a 2-inch overhang on 2 sides. Butter or lightly grease the foil or parchment.
Stir together the graham cracker crumbs and 2 cups of the coconut. In a microwave-safe bowl, place both kinds of chocolate, 3 tablespoons sugar and butter. Microwave for one minute at 50% power. Stir. Repeat the process, stirring after each minute, until the chocolate mixture is melted and smooth. Let the mixture cool slightly until lukewarm to the touch. Quickly whisk in one egg.
Stir the chocolate mixture into the graham cracker/coconut mixture. Press evenly into the bottom of the prepared pan. Bake until set, about 10 minutes. Transfer to a wire rack, and let cool in pan.
Meanwhile, in a large bowl with an electric or hand mixer, beat the cream cheese and remaining 1 cup sugar on high speed until very smooth and fluffy, about 5 minutes. Reduce the speed to medium, and add eggs, 1 at a time, until well combined. Scrape the sides of the bowl as needed. Beat on medium-high speed until completely smooth, about 3 minutes.
Pass the cheesecake mixture through a fine-mesh strainer into a bowl, and stir until smooth. Pour over cooled crust. Sprinkle remaining 1 cup coconut evenly over the top. Bake for 32-35 minutes, until the top layer is just set and golden brown. Let the bars cool completely in the pan on a wire rack. Refrigerate, loosely covered, overnight.
Run a sharp knife around edges of pan, and use parchment or foil handles to lift out the cheesecake. Cut the bars into 1-inch squares. The bars will keep up to 4 days in an airtight container kept in the refrigerator.