My great grandfather John Wesley Burleson was a sharpshooter in the Civil War, and he was said to be super accurate with his long caplock rifle.
This is his only surviving known photo, he does not look too happy:
J. W. Burleson, circa 1925
The foremost Civil War sniper rifle was the British “Whitworth”, a Civil War confederate "sniper rifle" that used a hexagonal barrel with hexagonal bullets:
If you can find a Whitworth rifle for sale, expect to pay over $70,000.
Check this out, a Civil War rifle being shot at 420 yards. Amazing!