Jacklord
You could use a conical minnie ball but the recoil will be brutal.
Several of our members have, I believe, cracked their pistols stocks by using heavy projectiles or heavy powder loads.
I agree with mark/wi that a patched roundball would be the best choice.
For loading a pistol, I recommend that you use a thinner patch than the rifle shooters like.
Many of them like a .018 to .020 thick cotton cloth patch for their rifles but this makes a very tight patch/ball combination.
Although it loads fine in a rifle, it can proove to be very difficult to start into the bore of a pistol and ram down to the powder charge.
For this reason (and the pressures in a pistol are much less than a rifle) I recommend a .012-,015 thick cotton patch.
Just make sure the patch thickness is greater than the rifling depth of your gun. (Dixie Gunworks says the rifling depth in the Great Plains Pistol is .008 deep.)
If you plains pistol is a percussion style you can use either real black powder (best) or one of the synthetic black powders like Pyrodex.
If you use a synthetic powder try to get the MAGNUM style caps. They work better with these pseudo powders.