I think we can narrow down the year to 1955 (or at least the year of the photos on the cards).
- Washington Nationals had that name up until 1955
- The Athletics moved to Kansas City for the 1955 season.
1955 is the only year that would be common across the stadiums (e.g. NY Giants, Brooklyn Dodgers, Connie Mack Stadium, Washington Nationals and the KC A's.)