Preheat oven to 350 °F (175 °C). Line cookie sheets with parchment paper.
In large bowl, stir together sugar, oats, cereal, flour, baking soda, baking powder, salt and allspice.
Make well in centre and pour in canola oil, applesauce, egg whites and vanilla. Mix until well blended. Stir in sunflower seeds and cherries. Roll cookies into golf ball-size balls. Place cookies 2 inches (5 cm) apart onto prepared cookie sheets and flatten to 1/2-inch (1.3-cm) thickness with wet hands.
In preheated oven, bake 8 minutes for chewy cookies. Remove from cookie sheets to cool on wire racks. They store well in freezer.