The 1867/96 was the rimfire to centerfire conversion of the original RBs. Your rifle should have a crown on the top of the barrel, between the rear sight and the receiver. This was added when the centerfire conversion was made. Check carefully what the chambering is now.
For shooting, it is important that the face of the block is square to the bore axis - and remains so after the shot has been fired!
Check that no live cartridge is in the chamber. Cock the rifle and check that the block face is square to the bore axis. Now any mechanical system must have some play, however small, in order to function. And then wears as it gets older. The weakness of a worn RB is that this can mean that the block face is no longer square to the bore axis after firing. Get a (preferably brass) rod about a yard long that will slide down the barrel. "Fire" the rifle, so that the hammer moves fully forwards and locks the block. Insert the rod into the barrel and push it down very firmly. The block will appear to move back slightly, but since it is on a pin it will actually rotate a little. And if pin/block wear is excessive, the block face, no longer being square to the bore axis, will cause the base of the fired case to be slightly skewed. Basically, if you can see that it is no longer square to the bore, then you have a problem, as every time the case is fired the base will be distorted again.
Assuming that the distortion is small enough that it does not present a safety problem, the simple answer is to mark the cases so that they are always inserted with the same orientation, so that any slight skew remains constant and does not cause a repeated reworking of the base area. And do not fully calibrate the cases either! Treat all old BP rifles as individuals, forget about modern notions of headspace, and regard the first firing as a fire-forming to make the cases fit that rifle. For subsequent firings use neck-sizing only. OK, so the case has no neck - you simply screw out the sizer half a turn.
Best of all, if the chamber/bore dimensions allow it, is to use lead bullets with about 5% tin added and a diameter that allows them to be seated without resizing the case at all. This is a single-shot rifle, so neck tension can be very light - a finger-and-thumb push fit is enough - as the sheer inertia of the heavy bullet (weight somewhere around 400-520 gns) ensures adequate case expansion, and the 5% tin alloy is soft enough to slug up to fit the bore, even if it is noticeably worn. Some experimentation will be required to find the best match.
But...
Do NOT use nitro propellants.
Do NOT use jacketed bullets.
Both of these will send pressures up to potentially dangerous levels. And put together they will endanger your life. You are firing a barrel that was intended for BP pressures when it was new, and it is now 150 years old!
And to anyone who now writes in saying that he uses nitro and his RB hasn't failed, I can only add the word ... yet.