James, look into the .50-70 Government (.50 Musket). Introduced in 1866, used in Springfield single shot (trapdoor) rifles until replaced by the .45-70 in 1873. A friend of mine has one, although I'm pretty sure his rifle is a reproduction 1873 model.
The cartridge satisfies the 1870 or earlier requirement, and can be loaded with black powder or some smokeless. I have a couple loads in my books using IMR 3031 and IMR 4198.
You would have to do a little research about which Springfield single shot model is correct for a pre 1870 design. I'm no expert on them. I'll ask around, might know more in a few days...
I will add that, when you do find a reproduction of a suitable gun by design age, that you obtain documentation of the design history, because it sounds like you will have to obtain a decision/approval from a govt agent, who, in your situation is most likely NOT going to be well versed in arcane firearms lore. See if you can get a book (or several) on the rifle, so you have something "official" to show that it actually was designed before 1870. Perhaps even better, have your local library get a copy of the book (pay for it yourself, if you have to) and then, if the govt official wants some kind of "proof" you can tell him about how the proof is in a book in the library, which he can check out and read himself. It will seem more "official" that way.
A library book carries more weight to the un/under informed than some helpful web site. Just a thought.