Howdy
Uberti makes a replica of both the 1860 Henry rifle and the 1866 Winchester.
The Henry rifle was the predecessor of all the later Winchester lever action rifles. It was produced by the New Haven Arms Company. The design was patented in 1860, actual production did not start in earnest until about 1862. Production ended in 1866 with the introduction of the 1866 Winchester. The originals fired the 44 caliber Henry Rimfire round, a copper cased round carrying about 28 grains of Black Powder and a 200 grain bullet. This was the first successful lever action repeating rifle, although it was in part based on the earlier Volcanic rifle.
http://www.uberti.com/1860-henry-rifle
Since the Henry round is no longer commercially produced, the current replicas are chambered for 44-40 and 45 Colt. These rounds are slightly longer than the original Henry round, carrying more powder and producing more power.
Here is a photo of my replica Henry. Mine has the 'iron' frame, actually steel. Most of the originals had bronze frames. Mine is chambered for 44-40, I only shoot it with Black Powder, and I shot it today in the last Cowboy match of the year.
Uberti also produces a replica of the 1866 Winchester.
http://www.uberti.com/1866-yellowboy-rifle
Oliver Winchester was the chief stock holder of the New Haven Arms Company, and in 1866 he changed the name of the company to Winchester Repeating Arms Company after a dispute with Benjamin Tyler Henry, the designer of the Henry rifle. The 1866 Winchester also fired the 44 caliber Henry Rimfire round. Modern replicas are chambered for 44-40, 45 Colt or 38 Special. The 1866 Winchester was the first rifle to employ the King's Patent side loading gate that was used on almost all the later Winchester lever action rifles. It was also the first lever gun to have a wooden fore end. Because of the brass frame, it was often referred to as the Yellow Boy. Not to be confused with the 22 caliber Golden Boy rifle currently produced by the company that masquerades as the original Henry company. The Model 1866 Winchester was produced from 1866 until 1898.
Uberti also makes a replica of the Winchester Model 1873, but that is after your cut off date.
http://www.uberti.com/1873-rifle-and-carbine
Although all of these rifles can be fired with Smokeless powder, they were designed during the Black Powder era and all originally fired cartridges loaded with Black Powder.