I saw this over the weekend on a visit to Buffalo Gap, Texas. It is housed in the original Taylor County Courthouse, built in 1879. I couldn't find any information on this smoothbore, but here is a side view and a shot of the only marking I could see in the available light, the number 1202 on the muzzle:
By the way, here's the courthouse, where my great-grandfather and great-grandmother were married in 1880: