Sec. 2. It shall be unlawful for any person to carry any sling shot, billy, dirk, pistol or any concealed deadly weapon or to discharge any firearms, air gun, sparrow gun, flipper or bean shooter within the corporate limits of the city, unless in self-defense, in protection of property or an officer in the discharge of his duty; provided, however, permission may be granted by the mayor to any person to carry a pistol or revolver when upon proper representation it appears to him necessary or prudent to grant such permission.