Here is a fantastic map, made by the G.M. Hopkins Company in 1923 and available from Pitt’s Historic Pittsburgh site, showing “Central Amusement Park,” complete with grand stand, on exactly the spot hypothesized the other day, on the south side of Wylie Avenue between Junilla and Chauncey. In those days Hallett Street cut all the way through from Junilla to Chauncey, so Central Park was bounded by Humber Way on the north, Chauncey Street on the west, Jacobus Way on the west, and Hallett on the south.
Also, looking through the maps at Historic Pittsburgh, it appears that the current Josh Gibson Field is actually located a block west of the historic Ammon Field where Gibson and the Crawfords played in the late 1920s and early 1930s (and which did not exist at all in 1923). I’ll post more about this in the next day or two.
UPDATE 1:16 a.m. It’s unclear where the exact boundaries of the park were, by the way, but any way you look at it Central Park was evidently quite tiny.