Gary is right on this one I think. Your pewter "C" has no serif on the upward hook of the "C" which from all the examples of the Confederate Calvary Coat Button I found (which is the closest military type of C button yours comes to) do not have the symmetry that your C has, in addition to what Gary already mentioned about the C being far too open between the hook ends and is overall a more block style letter. Now, having said all of that, there indeed were variations of the Confederate Calvary Coat button which were different than the real deal example I will use below. But, even in those variations, for example, a script "C" button or just different C altogether, all the examples had some sort of variation of a serif (but a defined serif) on the top hook of whatever style "C" that was used.
Another thought, and I may step into it with those on TNET that are better button identifiers than I am, is that for one, cast pewter buttons really were not used a whole helluva lot on either side. It's not to say they weren't at all used but the few examples I did find were 1) french made "Chausseur" style buttons which are not these or 2) crudely made pewter but nothing that matches up with yours specifically. Second, it appears your button has a "self shank" back to it and while that method was around at the time of the Civil War, not many buttons that were made specifically for military use were made that way.
What I can share is for CW reenactors, there is the following website that sells fairly poor quality cast "C" pewter buttons that are a little closer to your type, though I think even saying that much is a stretch, but nonetheless they are available. If your buttons are indeed repros, they are at least better quality than these...
Pewter Block 'C' (Cavalry) Button
A nice example of the button I referenced that was used by the Confederacy was made by HT&B/Manchester
and back...
At the end of they day, still cool cast pewter buttons. Probably for civilian use, possible it predates CW but more likely made afterwards.
Nice find!
-H