It depends...
Assuming *proper shot placement*....
The 45 is certainly adequate. I consider the 50 a good minimum for deer either Whitetail or Mule deer. If you hunt in the west a 54 might be better. If you hunt on a 40 or 160 acre lease in the east you might want a 62 to make it little less likely they will get off the property.
Deer can be very hard to stop. I have had them cover 200 yards when dead but didn't know it. Both 50 and 54 and the range was short both times. I could not believe the whitetail shot with the 54 could run off but she did and at high speed. Died mid leap, landed dead and slid to a stop on the snow and never wiggled. But I have seen them go 150-200 shot with 7mm mag with chunks of lung out the exit hole...
First deer my son shot was at 40 yards+- with a 45 flint with 45 grains of FFFG. The deer went maybe 75 yards shot just over the heart. Ball did not exit.
Any of them will work. Just do not expect the deer to fold at the shot. Unless the nervous system is interrupted or shocked they are not likely to go down in their tracks no matter what they are shot with.
If you re-enact something that "fits". Most original Kentuckies with rifling top out at about 50 caliber, some are bigger many are smaller. But the 50 is a very nice caliber for deer sized animals. It will kill deer reliably about as far as you should be shooting with a RB.
But the final choice is yours. Pick the style you like and then use a caliber appropriate to the style. Some Golden age stock designs are not all that good with calibers over 50 unless the rifle is fairly heavy. Some can cause grief as 45s. At least some pre-carves. Using a 50 allows a lighter rifle than the larger calibers do. If you want a 62 or bigger you will generally be better served in building an appropriate English style rifle or a well designed German Jaeger. Over 62 it gets very important. 62s get into the realm of nasty with a stock not meant/designed to handle recoil well. So the stock design and caliber really need to be paired for best results. Recoil can get into the 375 H&H realm or even worse with the larger bores. 66 and up.
If you want a 54-58 both good choices for a heavy kentucky choose a stock design from the early American guns with fairly flat comb lines, a wide buttplate and use a c weight swamp.
A 495 ball will weigh 180 grains, the 535 about 225-230, the .615 is about 350, a .662 ball weighs 437 a 735 ball will get close to 600 IIRC. The recoil will go up in proportion, or worse, if the velocity is kept about the same. All will give good one shot kills on deer and even elk.
Picking a golden age stock design and building a light 54 or 62 can make for a very uncomfortable rifle.
Make you choice practice with the rifle and then hunt. Practice and familiarity with the rifle is more important than caliber.
For those worried about tracking the deer and blood trails etc. When broadside standing up with the legs normally placed shoot them right over the front leg 1/3 of the way down the body from the top of the shoulder. This will anchor about any deer if bone, shoulder and/or spine, is hit.
Yes its kinda long but there is no simple answer to this. It just SEEMS simple.
Dan