Stir together the first 7 ingredients until blended. Then reserve 1 cup molasses-coffee sauce in a small bowl; set the reserved sauce aside.
Trim ham, and, if desired, score in a diamond pattern. Place ham in a lightly greased 13- x 9-inch pan. Pour remaining molasses-coffee sauce evenly over ham.
Bake, on lower rack, at 350° for 2 hours or until a meat thermometer registers 140°, basting with sauce in pan every 15 minutes. Cover loosely with lightly greased aluminum foil the last 30 minutes to prevent excessive browning, if necessary.
Remove ham from baking pan; let stand at room temperature 30 minutes. Heat reserved molasses-coffee sauce, and serve with ham.
Molasses-Coffee Glazed Turkey Breast: Substitute 1 (5- to 5 1/2-pound) bone-in turkey breast with skin for ham. Place turkey in a lightly greased 11- x 7-inch pan. Proceed as directed, covering loosely with aluminum foil before baking. Bake at 350° for 1 hour; uncover and bake 1 to 1 1/2 more hours or until a meat thermometer inserted into the thickest portion registers 170°, basting with molasses-coffee sauce every 15 minutes. Serve with warm reserved molasses-coffee sauce. Makes 10 to 12 servings.