Use kitchen shears or a sharp knife to cut gumdrops into small pieces, drop into a bowl of sugar, toss to coat. Remove from sugar, allowing excess sugar to fall back into the bowl.
Preheat oven to 350 degrees.
Cream margarine and sugar together until fluffy. Mix in eggs and vanilla. In a separate bowl whisk together flour, salt, baking powder and baking soda. Stir dry ingredients into the wet mixture just until blended.
Stir in half of the gumdrop pieces. Scoop out 2 tablespoons of dough. Place on a parchment paper lined baking sheet. Flatten cookies. Top with more gumdrop pieces.
Bake 8-12 minutes until tops of cookies look dry, but edges are not yet browned. Cool on cookie sheet for 2-3 minutes, then move to a cooling rack to cool completely.
Store in an airtight container for 2-3 days or wrap and freeze for up to a month.