I didn't pay attention to the bands which are Type 2 M1863, but the barrel and hammer are definitely M1861. The picture isn't clear enough to make out the fit between the bolster and the lock. The bolsters were slightly different between the two models and this lock appears to possibly be cut out for the '63 bolster. If the date is 1864, that would settle the matter as far as that is concerned. 1863 would be ambiguous as both models were made in that year. Another clue as to the model is the shape of the ramrod channel at the muzzle end of the barrel. It was wider on the '55 and '61 models to accomodate the swelled ramrod used on those models. It acted as the retainer to keep the ramrod from sliding out. Conversely, the stock of the '63 had a ramrod spring or "spoon" to hold the ramrod in place.
Another thing about this particular piece. It has band springs. That definitely rules out a Type I '63 stock which used clamping bands. The picture isn't clear enough even when I zoom to tell. It does appear that they are this type, but I might just be seeing shadows. At any rate, the existence of a ramrod spring or lack thereof and the widened ramrod channel should make ID easy.
In any case, this gun is a mixed parts weapon. I had one like this with an 1855/61 stock, 1861 lock with a Type II hammer and a Special M1861 barrel, a reproduction '63 ramrod and '63 Type II barrel bands, one of which was reproduction. These guns appeared in the War as "cleaned and repaired" arms and after the War as "put together parts guns". From what I've seen over the years, many of these pieces have mixed parts on them.