Mix yellow cake mix, butter, 1/4 cup shredded coconut, and eggs together in a large bowl until creamy.
Drop teaspoonfuls of the yellow cake mixture onto ungreased baking sheets. Make a slight indentation in the center of each cookie with 2 fingers. Sprinkle 1/4 cup coconut on top; press gently into the center. Place a maraschino cherry in the center of each cookie.
Bake in the preheated oven until edges look dry and bottoms are golden, 8 to 10 minutes.