Proper seating of a conical bullet in a cap and ball revolver chamber requires a heeled bullet. That is, a bullet with a slightly reduced diameter base for a short distance up from the base, to start the bullet.
Years ago I played around with the Lyman 37583 bullet, a conical bullet of about 145 grains. This is designed like a standard bullet, with no heel to start in the chamber.
Accuracy was poor because I struggled to get the bullet started straight in the chamber.
The old, original conical bullets designed for cap and ball revolvers had this heel, to aid seating in the chamber. Without it, you struggle to keep the bullet from tipping while being seated. It's simply too much of a pain in the patoot to use a bullet without a heel.
Frankly, I've yet to find a conical bullet as accurate as a proper diameter ball. In the .36s this means .380 inch instead of .3755 inch. In my .44s I use .454 and .457 inch balls, instead of the recommended .451 inch.
Accuracy is better, and the ball clings better to the chamber, staying put during recoil and not shifting forward.
Some years ago, I read an article of a man who used both a Ruger Old Army and a Colt Dragoon reproduction with jacketed bullets seated over black powder. In order to do so, he had to ream the chambers of both revolvers to .450 inch, and use .451 inch bullets. Then, he built a powerful bullet seater that forced the jacketed bullet into the chambers.
The rammer under the barrel was probably incapable of doing so, because it required quite a bit of force to push the copper jacketed bullet into each chamber. You are, in effect, swaging the bullet diameter down to the diameter of the chamber: easy with soft lead, not so easy with a copper jacketed bullet.
Accuracy was no better than a lead bullet. He also noted that ramming the bullet into the chamber often resulted in the opening of hollow point bullets being swaged shut, so it wouldn't function.
He concluded it was an interesting experiment but not worth all the trouble.
And, because he was forced to ream out the chambers of his revolvers, he had to use much larger lead balls from then on.
Every once in a while I read in message boards where someone asks about using non-standard bullets in cap and ball revolvers. Forget it, they're more trouble than they're worth.
I have that article somewhere in one of my Handloader's Digest books, but it's late and I'm too tired to dig. I referred to this article about two years ago in a message board, when I had it before me for reference. A search may find my earlier post on this subject.
Lee makes a mould for an excellent conical bullet, but I'm uncertain if anyone actually offers the bullet. I cast my own, from dead-soft lead.
The Lee design has a heel on the bullet to help start it straight in the chamber, and its bullet bands are progressively larger from rear to front. The rearmost band is not much larger than the chamber, also helping with alignment. The forward band is full-sized, to ensure a good seal in the chamber.
The Lee is the only conical bullet I've found that can rival, and sometimes slightly exceed, the accuracy of a ball.
For most uses, however, the ball is ample. It's accurate, will punch a clean hole in cans and paper targets, and will take small game well if placed in a kill zone. It's also easier to load.
Old, original conical bullet designs, such as those once offered by Colt, Remington, Starr and others, are available as bullets from Dixie Gun Works. I've played with these too, but accuracy is lacking compared to the ball.
But order a variety if you like, and play with them. I did some years ago, and concluded that the ball was still best.