Women's History and Nineteenth Amendment Centennial Quarter Dollar Coin Program Act This bill requires the Department of the Treasury to mint and issue quarter-dollar coins in commemoration of the ratification of the Nineteenth Amendment granting women the right to vote. The design on the reverse of each coin shall be emblematic of the accomplishments and contributions of a prominent woman who was a resident of a state, the District of Columbia, or a U.S. territory. Such coins shall be issued in alphabetical order of the area represented, starting with the state of Alabama. Treasury shall: initiate a program to promote collection of the coins and recognition of their subjects, and strike and make available for sale silver bullion coins that are the exact duplicates of the coins.