Would have been .577 Snider, .450 Adams or .50-70 Government, all in 1866. The .45-70 actually originally used the Benet internal primer system, where the primer was inside the case and the firing pin punched through the base to set it off, they didn't change to the standard Boxer primer until 1882.
The .52 Maynard Cabine, introduced in 1860 and used in the US Civil War, was almost a centerfire, but it was externally primed. An external tape primer sent a flame through a pinhole in the base of the cartridge.
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