Combine margarine and molasses in a small saucepan, and bring to a simmer over medium-high heat. Remove from heat, and pour into a bowl. Add brown sugar, ginger, cinnamon, and allspice, and beat at medium speed of a mixer until blended. Gradually add flour, beating until well-blended. Cover and freeze for 15 minutes.
Lightly coat hands with cooking spray. Shape 1 1/2 teaspoons dough into a ball; repeat to make 24 balls. Roll balls in sugar, and place 2 inches apart on ungreased baking sheets; flatten cookies with the bottom of a glass. Bake at 350° for 8 to 10 minutes. Let cool for 5 minutes on baking sheets. Remove from baking sheets, and let cool completely on wire racks.
