Here is some more dating evidence.
Elisha Cook Jr. (1903-1953) played Frank "Stonewall" Torrey, and so should have been about
47 to 48 when Shane was filmed in 1951.
If Torrey was named after Stonewall Jackson that would have been after Stonewall Jackson got the "Stonewall" nickname in 1861, which would make Torrey's aged 47 to 48 in about 1908-1909, or later.
But "Stonewall" is Torrey's nickname, not a real name, so that is no clue. Since Torrey is an ex Rebel soldier, he should have been aged about 18 to 45, the age range of the vast majority of Rebels, in 1861-1865, and thus have been born in 1816 to 1847, and thus aged 47 to 48 in 1863 to 1895.
The settlers were homesteaders, and the First Homestead Act of 1862 would be the earliest possible date for Shane.
Ironically, one of the few restrictions in the Homestead Act was that the claimant had to have never taken up arms against the US government, which means that ex Rebel Torrey would not have been eligible for a homestead (unless he planned to lie), which means he wouldn't have tried to become a homesteader and would never have been gunned down, unless he was planning to lie.
Anyway, I am still hoping that someone will point out evidence in the movie that will give a more precise date range.
Added May 12 2019 - Seeing part of Shane recently, I noted that in the first discussion between Ryker and Mr. Starrett, Starret mentions that a penitentiary is being built.
The cornerstone for what became Wyoming’s first state prison was laid in 1888, two years after the territorial Legislature approved a $75,000 appropriation, but the prison itself did not open for 13 more years. Poor economic conditions caused the funding and construction delay.
Thus funds for the Wyoming Prison in Rawlins were appropriated in 1886 and the first prisoners entered it in 1901.
That may indicate that Shane happens in 1886-1901, a time span which includes the Johnson County War in 1892.
It is said that a federal Prison in Laramie, Wyoming was used for territorial and state prisoners before the State Prison opened. It was called the Wyoming territorial Prison.
The prison was built in 1872 and began accepting prisoners in early 1873. The facility had problems from the outset, with a fire in 1873 and recurrent jailbreaks. Of the 44 prisoners accepted in the first two years of operation, 11 escaped. By 1877 the prison was overcrowded. As the prison filled its reputation worsened, and it became less used, being considered more appropriate for those with light sentences. During the 1880s the prison was under capacity, with as few as three prisoners at one time. However, in 1889 a second cellblock was constructed, a expanding capacity to 150 and providing a central kitchen, dining hall, guards' rooms and steam heat. There were at least five cells for female inmates, and several solitary confinement cells. In 1890 Wyoming became a state and the facility was transferred to the new state, which already had planned a new facility in Rawlins. Butch Cassidy was incarcerated here in 1894-1896. Prisoners were transferred to Rawlins in 1901, The prison was closed in 1903 and given to the University of Wyoming.2
Thus it is possible that Starrett was referring to the prison in Laramie, which would date Shane to 1872 to 1873, or possibly to earlier years if it took years to build the prison.
In that same conversation Ryker said that he had a new contract to supply beef to the reservation and so needed to use the entire valley to graze his larger herds.
The Shoshone Indian Reservation was established in Wyoming in 1868 by the Fort Bridger Treaty Council. But the Shoshones mostly stayed near Fort Bridger for several years until the danger of hostile Indian attacks lessened. in 1878 the Northern Arapaho, former enemies of the Shoshone, were also placed on the reservation, which was renamed the Wind River Reservation.
Obviously Ryker would have made his beef contract with the Indian agent at the reservation, sometime after the agency was established on the reservation, unless the contract was made with an Indian bureau official with authority over a wider area. I guess that the early 1870s would probably be the earliest possible date for making that contract.
So those are a few more clues about the fictional date of Shane.