When Does the Film "Jonah Hex" (2010) Take Place?
"Jonah Hex" is a fantasy historical fiction film written by William Farmer with Mark Neveldine and Brian Taylor [loosely adapting "Jonah Hex: Two-Gun Mojo" #1-#5 (1993) by Joe R. Lansdale] that released June 18th, 2010. So when is "Jonah Hex" set?
It takes place on the fictional DC Films timeline in the year:
We know this because early on the real-world United States of American President Ulysses S. Grant makes an appearance during his time in office as president, which lasted from March of 1869 AD to March of 1877 AD.

1876 AD
We know this because early on the real-world United States of American President Ulysses S. Grant makes an appearance during his time in office as president, which lasted from March of 1869 AD to March of 1877 AD.
More specifically, during the President Grant scene, it's said: "There are centennial celebrations being prepared in more than 20 states.", referring to the celebration of the United States of American founding's 100th anniversary and the American Revolutionary War began in 1776 AD. Another characters later says, "America gonna be 100 years, Jonah."
1776 + 100 = 1876.
Additionally, there are multiple flashbacks that take place 6 years previous to the main action of the story. We know this because Quentin Turnbull says, "And l hear them, Mr. Lusk, as I've heard them for six long years.", referring to his feelings since the events of the prologue. That puts it in 1870 AD.
1876 - 6 = 1870.
Other flashbacks are specified as taking place during the American Civil War, which lasted from 1861 AD to 1865 AD but are otherwise unplaceable.
It is the earliest chronological film in the DC Films multiverse timeline and can be watched either at its timeline point or entirely separately.