I got this postcard today:
Some initial Googling indicates that the same publisher, Jessie D. Allardice, put out color tinted postcards of the park around 1915. If I really wanted to date this I'd probably have to start digging through the ProJo archives, since the photos are copyrighted to the paper.
my initial guess is that the field was above where the Temple to Music is now:
That's the only place that I can think of that has that natural amphitheatre shape, but they've probably moved a lot of dirt around in that park in the past 100 years or so.
One particular feature that is interesting to the vintage base ball player is the amount of space behind home plate, or the lack thereof. We fret over the fact that 19th century fields generally had more room in foul territory -- in part I suspect because baseball evolved from bat and ball games where the ball could be hit in any direction -- than modern fields, especially the softball fields we often end up playing on. I wonder when playing in smaller lots like this became more common, and how common it was in the 19th century.