Howdy, Pard,
The first thing you MUST do is have the gun checked over by a gunsmith who really knows what he's doing! Unfortunately, I don't know who might be able to do that, but you might be able to find one by asking on ALL the forums.
I would strongly recommend having the barrel and receiver tested using non-destructive testing, such as magnetic-particle or other appropriate methods. The receivers on these guns are effectively wrought iron, rather than true steel. The barrels are generally mild steel. But age and corrosion can result in weak spots, which NDT might be able to pick up. Still, on guns approaching 140-145 years old, you pays your money and takes your chances!
So far as the mechanics of converting to centerfire are concerned, S&S says that their breechblock will fit 95% of most Spencer military rifle/carbine receivers. The other 5% will require fitting of the block. The one I fitted some years back was one of the latter. Now I can barely file a flat surface, but by careful study and filing and fitting, I was able to get the block to work okay.
The next thing is to fit up the firing pin. I would recommend buying SEVERAL firing pins and strikers. I set mine up according to the instructions as an inertia-type firing pin. (With the hammer fully down, the firing pin doesn't project from the breechblock face, being retracted by a spring. When the hammer falls, the firing pin flies forward with enough force to fire the cartridges. (This is the arrangement used on the M1911 pistol!)
The third thing is to change the existing round-nose steel follower to the FLATNOSE BRASS FOLLOWER sold by S&S. (A hard rubber one would be more to my liking!) You MUST also use FLATNOSE BULLETS, preferrably with a meplat (flat) of .250" wide! Failure to do any of these things COULD result in a magazine explosion, WHICH COULD RUIN YOUR WHOLE DAY!
And, of course, you must obtain ammo. There is .56-50 being made. If you are converting a .56-56 (M1860), you may need to ream the inside of the case necks, and use a .535" bullet.
I hope this helps a bit, Pard!
Ride careful!
Trailrider