Here is Palace of the Fans in Cincinnati and here are the two side by side. Sure looks very similar but Palace of the Fans opened in 1902 and had corinthian columns like the postcard and an upper deck.
The stadium prior to that was League Park in Cincinnati. Looks like this might be the one. 1884-1901. League park burned down which then was replaced by the ornate Palace of the Fans.
http://en.wikipedia.org/wiki/League_...8Cincinnati%29