In a large bowl, with a mixer on medium speed, beat 1 1/2 cups butter, sugar, orange peel, and vanilla until smooth.
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. Mix in cranberries and coconut.
Shape dough into 1-inch balls and place about 2 inches apart on buttered 12- by 15-inch baking sheets.
Bake in a 350° regular or convection oven until cookie edges just begin to brown, 8 to 11 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.
Nutritional analysis per cookie.