In a large bowl, with a mixer on medium speed, beat 1½ cups butter, sugar, orange peel, and vanilla until smooth. Beat in egg, until well blended.
In a medium bowl, mix flour, baking powder, and salt. Add to butter mixture, stir to mix, then beat on low speed until dough comes together, about 5 minutes (see notes). Mix in cranberries and coconut. Note: The mixture may look dry until it comes together as a dough. If its too crumbly to form into balls, the dough need to be mixed longer; it should be a smooth homogeneous mass.
Shape dough into 1-inch balls and place about 2 inches apart on buttered 12×15-inch baking sheets.
Bake in a 350°F regular or convection oven until cookie edges just begin to brown, 11 to 15 minutes (shorter baking time will yield a chewier cookie; longer baking time will yield a crispier cookie). If baking two sheets at once in one oven, switch their positions halfway through baking. Let cookies cool on sheets for 5 minutes, then use a wide spatula to transfer to racks to cool completely.