1830-1865.
Roughly the mid Rocky Mountain trapper thru the California Gold rush and the Civil War.
Before all you Hawken lovers start to pounce on me, I feel totally safe in saying that not all of the Mountain Men had Hawkens. In fact, most did not have them.
The half stock rifles became very popular during the period I mentioned.
Percussion rifles became very popular during this period as well.
There were half stock rifles that only had one barrel wedge holding the barrel onto the stock during this period.
All of the reenactors of the Mountain Men I know (except for a very few who think that only the Hawken was used) accept guns like this as being Period Correct in their get together's.
Their only real and justifiable objection will be the adjustable sights if the gun has them.