I would say about the 1880's and 1890's.
I know at least with the Winchesters, the pistol grip with checkering was reserved for the delux model guns only.
If you look at Parker for example, Almost all of the guns prior to the 1880's had straight stocks on them. Then they changed.
Not sure exactly what triggered the change.

The prevelance of the straight grip might have just been a hold over from the muzzleloading days.

B.Dudley