Getting back to the original question, first off I have never seen a photo of a 1830-1840 half stock with a peep sight that I think was original to the gun.
Quoting Ned Roberts book
THE MUZZLE-LOADING CAP LOCK RIFLE BONANZA BOOKS, NY 1952,
"Practically all the flint-lock and percussion-lock hunting rifles that had been in use by the pioneer hunter-riflemen up to about 1840, were fitted with the simple open front and rear sights...The earliest attempt that I have found to improve these sights was on a Pennsylvania made rifle by John Henry, bearing the date of 1835, which had a low silver bead front sight, about 1/16 inch diameter and a very dark blue steel stem and two-leaf rear sight with U shaped notches having one leaf stamped "10" and the other higher one marked "20"...
Previous to about 1840, very few strictly target rifles had been made in this country as the demand for rifles up to that time had been for practical "all around" arms chiefly for use in hunting or war, and for this purpose the plain open sights appear to have been generally satisfactory... (pg 29)
Writing about the period after 1840 of a few guns made in the Eastern part of the U.S. :
"The hunting and target rifles...were fitted with the usual shaded pin-head front, an open V-notch rear sight, and a peep sight with folding disk top screwing into, the upper tang of the arm thus making them as near an "all around" rifle as possible..."
"There was quite a variety of folding disc top peep sights in use on rifles of this kind, each maker having a design that he, personally, considered the best. However, they were all made so as to permit folding the disc top down toward the muzzle, to allow the unobstructed use of the open rear sight in connection with the front sight when using the rifle for hunting purposes.
Certain makers instead of threading the peep sight though the upper tang of the stodk, and possibly weakening that, attached it to the breech of the barrel with small screws let into the long end of an L shaped piece of steel with the other vertical end extending some four inches back of the break-off, having a small peep hole in the center of it, through which aim was taken when using the rifle for target work..." (p 31)
Obviously I can't quote all that Mr Roberts had to say in his great book but it would appear that yes, some target shooters used peep sights however no mention of Plains style hunting rifles with them was made.
As for sights that come nearer to what "might" have existed, I'm sure the peep sight made by Thompson Center is much closer than the typical Micrometer scaled screw adjustable peep sights found on rifles like my Anchutz made by Lyman and others.
Although the TC peep sight doesn't come close to matching the type of sights Mr. Roberts speaks of, its simplicity IMO makes it a fair choice.
A TC style rear peep sight:
The "ladder" type sights that attach to the tang are good only for long range target shooting. The "ladder" also folds towards the butt of the rifle and will do its best to poke you in the eye if you fold it down and then shoot the gun.
A ladder style rear sight on my Tryon:
Another peep sight that is sold by Dixie Gunworks is period correct for certain target guns like my Schuetzen. This sight needs a very tall front sight to be usable.
Were I you, I would go with the TC tang mounted peep sight.