Sift flour, baking powder, baking soda and salt. Cream shortening, add sugars gradually and continue to beat until light. add well beaten eggs and vanilla. Combine the dry ingredients and creamed mixture, blend well. Add the chopped cherries.
Shape into 4 rolls and wrap each in wax paper. Chill in the refrigerator, at least overnight. (The dough can also be frozen and taken out as needed.
When ready to bake preheat oven to 400°F. Cut the roll into thin slices with a sharp knife and place on an ungreased baking sheet. Bake for 5 to 8 minutes.