A covering attachment or joystick cover for attaching to a joystick of a game actuation device includes a cover body having a top layer and sides extending downward therefrom. The sides are adapted to surround an upper portion of the joystick. The cover body includes an opening formed between the sides to receive the upper portion of the joystick. The sides of the cover body have a portion extending radially inward in order to attach the cover body to the joystick. The cover body has a first hardness. The joystick cover includes a cover cap positioned over the top layer of the cover body that engages the cover body sides, and has a second hardness that is greater than the first hardness. The joystick cover can also include an image plate that is positioned between the cover cap and the cover body that is visible through the cover cap.