This is the way my Mom makes 'em. Don't know whether or not it will make a difference for you, but Mom always insists on using Eagle Brand condensed milk for this recipe.
2 pounds powdered sugar
1/4 pound melted butter
14 ounces sweetened condensed milk
Work the above ingredients together with your hands.
Roll dough into small balls.
Make a hole in each one and place a cherry into each hole. Close the hole back up to cover the cherry -- make sure the cherry is completely covered.
Dip in melted chocolate.