Any coin-operated amusement device, including pool and billiard tables, operated in conjunction with any place of business may lawfully be operated and remain open for play during all hours that the place of business in which such device is located may lawfully remain open for business, provided however that not more than one (1) coin-operated pool and billiard table operate in each individual place of business outside the city limits of a city or town, and the presence of such coin-operated amusement devices shall not require any other license because of their presence, as long as they are incidental to the operation of such business and there is a valid coin-operated amusement device license for each such device. Provided that any incorporated city or town may, by ordinance, authorize and license family amusement centers offering pool and billiards to persons of all ages and either sex.