I did a bit more digging and a search lead me back to my own website (which it often does) and this comment from James Brunson:
Asa "Acie" Price the coacher for Walter L. Cohen's Pinchbacks came from St. Louis. In 1885, Acie and his brother, David, served as the St. Louis Eclipse Club battery. That same year, the Black Stockings and Eclipse Club put together a team that traveled to New Orleans and played all the local colored teams. Following this road tour, David Price returned to St. Louis and Acie stayed in New Orleans and played for Cohen.
In 1889 Price died of yellow fever and was buried in New Orleans. Only 23 years old, he was buried [in his] baseball uniform.
The information that I found in the census data stated that the Price brothers were born in Kentucky, David around 1863 and Asa around 1865. It appears that they were working in some kind of mill, although I found it difficult to read their occupation information.
The Price brothers are also mentioned in Brunson's excellent piece on Henry Bridgewater and the Black Stockings:
Throughout the season [of 1884], the Black Stockings faced many challengers, including the Eclipse Club, its chief competitor for the title colored champion. In late August, these colored clubs battled for the championship. Managed by Charles Brooks, the Eclipse Club included the celebrated battery of Acie Price and Dave Price. They beat Bridgewater's nine three straight games, the final contest witnessed by 2,000 spectators....
He also mentions that David Price played for Bridgewater's Black Stockings in 1887.
I have to thank Dwayne and James because, without them, I never would have seen how all of this information fit together. I may not have a lot of readers but the ones I have are pretty smart.