Preheat oven to 400 degrees. Mix shortening, sugar, eggs, and carrots. Mix flour, baking powder, and salt into shortening mixture. Mix in coconut. Drop dough by teaspoons about 2 inches apart on lightly greased cookie sheets. Bake 8-10 minutes or until no imprint remains when touched lightly. Cool and frost.
Frosting, Blend butter and sugar together. Add orange juice and grated orange rind. Mix till smooth.