To make rum balls, mix confectioners' sugar, cocoa powder, ground allspice, dark rum, light corn syrup, finely crushed vanilla wafers and finely chopped and toasted walnuts. Press the combined ingredients into balls, and drag through confectioners' sugar. Refrigerate before serving.
In a large bowl, sift 1 cup confectioners' sugar, 2 tablespoons cocoa powder and 1/2 teaspoon ground allspice. Stir in 1/2 cup dark rum and 2 tablespoons light corn syrup. Add 2 1/2 cups finely crushed vanilla wafers and 1 cup finely chopped and toasted walnuts. Mix thoroughly, and refrigerate for approximately 30 minutes until firm. The chocolate mixture can appear dry in consistency.
Pour another 1/2 cup confectioners' sugar into a separate shallow bowl or dish, and set aside.
Remove the chocolate mixture from the refrigerator. Ladle out small portions with a tablespoon, and shape into 1-inch balls. With your hands, coat the balls with the additional confectioners' sugar. Put the sugar-covered balls on a baking sheet. Lay plastic wrap over the sheet, and return to the refrigerator. Let sit overnight. To store the completed rum balls for a two-week period, place in an airtight container, and separate each layer with a piece of waxed paper to avoid sticking.