Great question for HB. The Ohio association was formed in 1887 but I would guess that some of the eastern States predate that. Hopefully HB will spot this thread and have the answer.
On August 22, 1890, the Pennsylvania State Sportsmen's Association was organized at the Crosby House in Corry, PA. This meeting was set in motion by H. A. Penrose, owner of Corry's Keystone Manufacturing Company, which made clay targets and traps