Preheat the oven to 400 F. Lightly spray a 24-cup miniature muffin pan with nonstick cooking spray.
In a medium bowl, combine the cornbread mix, milk, and eggs, stirring until smooth. Spoon the batter evenly into the prepared muffin cups. Bake until lightly browned, 10 to 12 minutes. Let cool in the pan for 5 minutes. Remove from the pan. Using a sharp knife, cut out the centers of the cornbread muffins to make a cup, leaving a 1/4-inch thick shell. Discard cornbread centers.
In a small bowl, combine the chicken and barbeque sauce. Spoon the mixture evenly into the cornbread cups. Garnish with chopped sweet pickles, if desired.