I'm not sure about the South Carolina specifically, but most of the Peabody carbines are 56-60 RF; same as the Spencer.  Providence Tool Company does conversions.  I have one and, asside from the horrible trigger pull, it is really fun to shoot.  I also have a Peabody carbine that is 50-70 which was converted from RF way back when.

Regards,
George

I think he just want's to convert his breech block to center fire.

I am no expert on Peabody rifles and carbines but, according to Hull (Providence Tool Company Military Rifles; 1978), the Canadian Peabodys was in 50-60 rimfire,   Hull also says that the carbines were produced in 45 and 50 Peabody rimfire, but he does not elaborate on which Peabody Rimfire.  Given the time that the South Carolina carbines were produced, it is more than logical that the 50 caliber ones were in 56-50 Spencer or the Peabody equivalent of that.  Every unaltered Peabody carbine that I have seen has been in the 56-50 chambering.

George
Salmon, Idaho

The OP asked if there was a centerfire block for his Peabody.  In this day of CNC machines, I'm sure that the answer is "YE$".

I also am a cartridge collector from the pre-Internet days.  Charles Suydam's 1960 book "The American Cartridge" is still a good all-round reference for the big rimfires.  On p. 134, he shows a photo of five .50 caliber rimfire rifle cartridges.  Specimens 1 & 2 are .50/60 Peabody rimfires.  There were big manufacturing differences, but they all were stuffed into the chamber.  #1 has dimensions close to the above photo.  Suydam wrote "probably by UMC".  #2 is a bit longer "possibly FA".  .50/60 Peabody rimfire cartridges were made by Frankford Arsenal for use by carpetbagger militia & police when South Carolina was occupied by Federal forces, 1865-1877.   

The Peabody cartridges are all about 1/4" longer than the Spencer cartridges and will have different weights.

Back again with another mouldy pre-Internet reference.  Fred Datig published 4 volumes of "Cartridges for Collectors" back in the late 1950s to early 1980s.  In Volume IV, privately printed in Switzerland in 1983, Datig has a chapter on Peabody Rimfire Cartridges (pp 140-145, with illustrations through p. 156).   

Datig states in two places that the .50/60 rimfires were developed at Frankford Arsenal "in the first half of the 1860s" and that the Providence Tool Company simply copied the design.  These were a series of incremental improvements in copper cased rimfires that rapidly led to the centerfire .50-70 Government cartridge.   

The Canadian Peabody contract of 1865, only slightly-post American Civil War, was for the then-likely military cartridge in production at Frankford Arsenal.  The development of drawn brass cartridge cases rendered the 50/60 rimfires obsolete by the late 1870s.  The Canadian contract was for 5,000 rifles.  That many were made, but only 3,000 were delivered and paid for.

The South Carolina order of 350 carbines in 1877 was supposedly for arms made for the Franco-Prussian war but not delivered.  But the Providence Tool Company had 2,000 of the Canadian rifles in the warehouse.  The Providence good old boys made a deal with the carpetbagger good old boys and South Carolina got their carbines in .50/60 Peabody rimfire.

That is why the OP is correct when he told us about the caliber of his carbine.

Last night I took a 56/50 spencer Rimfire Cartridge from my collection.   I found that this will also Chamber Into the carbine and will close  the block. 
JW

I am Currently away. Until Next week. The SC is stamped On the top of The But plate
I will get detailed Photo when I return