Based on original iron mounted guns that I have seen and read about, I believe the barrel and mounts were originally treated one of four ways; left white, blackened (coated in oil and heated over a forge until the oil burns off), browned, and charcoal blued. I have seen all of these on one gun or another, frequently mixed. They possibly could have been rust blued but a rust blue can pass for a charcoal blue if you are not too picky.
I usually treat all my iron mounted guns the same; I produce a nice gun metal gray patina on all the mounts and barrel. I also slightly age the stock by not worrying about all the accumulated dents and dings and applying a black wash with lamp black oil paint, my normal gunstock finish, and turpentine.
The metal finish is a fudge since I really don't know how a particular gun might have been originally finished. If I had to guess, I would say blackened or charcoal blued. The really nice guns were probably charcoal blued. I haven't done a charcoal blue because of the trench I would have to dig in the yard and the big charcoal fire I would have to build in the trench. Both of these can be problematic in a residential area, particularly during fire season. That said, I have a project coming in about six months where the client wants an as new iron mounted rifle where I will probably charcoal blue everything.
In order to get the nice gray/blue/black/brown patina I like, I degrease everything thoroughly, (Dawn or Acetone work equally well), apply an even coat of cold blue solution, and while still wet, I apply tincture of iodine. The iodine is an oxidizer, any oxidizer will do. I think put everything in my damp box. If you have held your tongue just right, you should have a red rusted mess the next day that looks like coral is growing out of our mounts and barrel. If you don't get the heavy red rust, let everything rust another day or two. If you still don't get a real heavy red rust, then you are going to have to scrub everything back to gray and do it over again to darken the patina. Then it is just a matter of scrubing back the rust to the desired color. I suggest not using anything more aggressive than a green ScotchBrite pad and that is only to knock down the worst of the rust. When you start to see some bright metal, switch immediately to a gray ScotchBrite pad and finish up with the White pad. You should end up with a gray/blue/black patina that may have some brown overtones.
Of course you can achieve the same result in many different ways. Scrubbing back a rust blue would do the same thing but would be a lot more work. I think bleach or any strong acid would do the same thing as the tincture of iodine, but the iodine seems relatively safer to me. You must use tincture of iodine and not poviodine. Poviodine (Betadine) has only about a quarter of the elemental iodine available for the reaction.
