Preheat oven to 325 degrees Fahrenheit, and line two cookie sheets with parchment paper.
Sift flour, baking powder, baking soda, and salt together. Set aside.
Cream butter until pale yellow and fluffy using an electric mixer. Then add sugars (both granulated and light brown) and continue creaming until the mixture is barely gritty when rubbed between your finger and thumb.
Blend in egg and vanilla extract.
Fold in the sifted flour mixture, using a spatula or wooden spoon, until the mixture is just combined.
Mix in the shredded coconut and butterscotch chips just until blended.
Drop dough by rounded tablespoons onto prepared cookie sheets, spacing about 1½ - 2 inches apart.
Bake coconut butterscotch cookies for about 15 minutes or until they are golden brown around the edges. Allow cookies to cool on baking pans for a couple of minutes before carefully transferring them to wire racks to cool completely.