Begin by preheating your oven to 350 degrees F. Use two 12-cup muffin pans and spray 18 holes with nonstick cooking spray and set aside.
To make the batter, first cream the margarine and sugar in a deep mixing bowl with an electric beater for 1 to 2 minutes, or until pale. Add the eggs and the cocoa powder and mix until smooth, then fold in the applesauce.
In a separate mixing bowl, combine the flour, baking powder, baking soda, and the salt, and then stir them into the egg mixture gently. Be careful to not over-mix.
Next, spoon the batter into the prepared muffin tins, filling each one 3/4 of way full. Bake for 22 to 25 minutes, or until a toothpick inserted into the center of the muffin comes out clean. Cool briefly before removing the cupcakes from the pan, and serve.