Using a hand-held or stand mixer, cream together the shortening, granulated sugar, and brown sugar until creamy, about 2 minutes
Pour in the eggs and vanilla extract and mix for 2 more minutes
Meanwhile, mix together the flour, baking soda, baking powder, and salt in a separate bowl
Slowly and in various additions, mix the flour mixture into the shortening mixture
Add the coconut and oats and mix just until combined
Place the cookie dough on a floured surface and divide into four logs. Wrap each log in plastic wrap and freeze for 2 hours or until firm
Preheat the oven to 350 F. Take the logs out of the freezer, unwrap, and cut each one into ½ inch-thick slices
Place the cookies in a baking sheet lined with parchment paper. Space them 2 inches apart and bake them for 10-12 minutes or until golden brown
Let the cookies rest for 5 minutes, and then transfer them to a cooling rack