ORIGINAL: cayugad
I browned a rifle I build almost 30 yards ago. It was a solution that came in a bottle. You had to steel wool the barrel, wipe it off with denatured alcohol, then smear this stuff on. Wait a while and it starts to rust the barrel brown. I had to do a lot of coats to get the color I wanted. I was looking at the rifle the other day and it needs to be re-done as the barrel is almost back to the White. Too many times cleaning I guess.
Birchwood Casey makes a Browning solution and I think Brownells makes one as well... you could look there also.
That Birchwood-Casey PLUM BROWN makes a very pretty brown color, but it is NOT an authentic rusting solution. It is more of an "instant brown", in that after polishing your steel up nice and shiny, and completely de-greasing the bare metal, you have to heat it up to a sizzling hot temperature then wipe the solution on in one pass before the partscool. The brown appears instantly, no carding or steel-wooling required. You then oil it (after it cools down), and it looks great on the barrels I've used it on. It seems to give a smoother, less porous appearing finish.
Dixie Gun Works (of course!!) sells their own browning solution, and it is a rusting solution. You use it like Cayugad described. There are a number of other brands of true "browne" that work similarly, including th Laurel Mountain Forge stuff that works WITHOUT having to degrease the barrel before applying it. I have used the Laurel Mountain product, and DGW's. Both produce a good, "Olde Tyme"brown finish if used exactly according to the directions.
The Angier book I mentioned previously contains MANY formulas for bluing and browning solutions, some that were the favorites of a number of old-time gunsmiths whose products have not been equalled in the past 100 years or so, except by one or two custom smiths!(Guys like A.O Niedner, Harry Pope, etc.)
When using a rusting solution, the only real difference in using it to produce a brown color or a blue/black color is that for the black color, the barrel/parts have to be boiled in pure, distilled water after each "pass" of the browning solution, after the loose rust is carded off. The boiling process changes the red oxide to black.
Good luck! This subject is a whole field of study by itself!!