I have chrony'd .454 round balls coming out of my "Pietta 58' remington Buffalo" revolver with a 12 inch barrel at just over 1000FPS. That is with 30 grains of fffg. I would trust this for deer within normal archery ranges, as I can break clay targets sitting on a fence 50 yards away with it.
I also have a 20 gauge flint lock "tower" pistol a neighbor gave me. I have never fired it, but I have researched it a little.
FOr many years during the fur trade pistols were made of the same caliber as rifles so the trapper only had to carry one size of ball. They could get all the way up to .69 caliber and down to .55 caliber normally.
These very pistols were sometimes employed in horseback hunting of buffalo. If you have ever seen an old Edison movie of Buffalo Bill's Wild West he even has a mock buffalo hunt firing blanks from his navy colts at running animals from horseback. I would believe it. If you can kill a critter with a bow and arrow, a big roundball should do the trick too.
Energy wise, I would say an old hose pistol on the 55+ caliber range could kill a deer with a chest shot, but only within mabey 35 yards. I would also say that if you are using a smooth bore pistol, as most of them were, you might want to consider a buckshot load, if you can get one to pattern well.
Actually, I should put that tower together and chrony it one of these days.
Edit: This thread got me really enthused. I grabbed the assorted pistol parts from under the couch and got some lock screws from the hardware store, bought some buckshot and flints, and spent the afternoon in the workshop ajusting screws with a file.
Now that it works, sort of, I had some fun down at the range. I made up a load of 45 grains of Pyrodex P and 6 00 buck pellets, and I can barely hit a grocery bag from 15 yards. Oh, and I found out that it is a .69 bore, not 20 gauge. May not be too accurate, but it;s such a blast to shoot I want to get some practice in with it and give it a real workout. I'll chrony it one of these days when I can be sure I'm good enough with it to not ventilate the chronograph.