My Uberti-made 1858 Remington will put six bullets into a 1-1/2" circle all day long, from a benchrest, at 20 yards (measured, not paced). The load is:
Lee 200 gr. conical bullet cast of very soft lead.
Goex FFFG black powder -- 26 grs.
Remington No. 11 percussion cap, pinched into elliptical shape.
Bullet lubricated with Gatofeo No. 1 lubricant: 1 part canning paraffin, 1 part mutton tallow, 1/2 part beeswax. All measurements are by weight, not volume.
The use of any other ingredients will result in an inferior lube. Use exactly what is prescribed.
My Uberti has a very nice trigger, aiding accuracy. At 25 yards, the groups remain the same or open slightly. This load could probably put all bullets in the same ragged hole, but the fixed sights and my 57-year-old eyes are not best of friends.