Rooster Cogburn carries a Colt Peacemaker/Single Action Army revolver. Developed in 1872, I assume it was adopted by the Army in 1873 from it’s M1873 nomenclature. The Peacemaker would have been in wide circulation by 1875, and remained popular for decades.
Also appearing in the film are a Winchester 1892 saddle-ring carbine, a Winchester 1894 saddle-ring carbine, a Henry 1860, a Sharps 1874 carbine, and a Winchester 1866 made to look like a Henry. Of course filmmakers are notorious for using anachronistic firearms in Westerns, and the Winchester 1892 in particular seems to show up in films set as early as the 1860s.
Let’s say Rooster Cogburn is about 50 or 60. We know he fought in the Civil War. Did he fight in the Mexican-American War? If so, he would have been born around 1830. So… True Grit takes place around 1880 or 1890?
I don’t have an answer except to say the Blu-Ray disc of the Coen Brothers adaptation we rented had extra features including one about the guns. The guy who handled selecting all the firearms goes into saying what year it’s supposed to be and the research into what weapons (both guns and knives) would be appropriate for that time and how they were selected.
So my gut reaction is that whatever year it is in the movie (at least the one from a couple years ago) represents it accurately.