What caliber air rifle for deer hunting?

.45 or .50, 

The .45 is going to have a flatter trajectory, the .50 has harder fpe 

I have hunted with both the .308 and 357 I am not saying they will not take a deer down but I do not like the time it takes to do so for boiler plate shots. 

Deer are some of the most unpredictable animals I have ever seen when it comes to kill shots, One will drop where it stands, another same shot placement will run 150-200 yards (or even further)

For me I like to follow Mr Hollowpoints suggestion and put a round through the shoulder and into the lungs this means you need the FPE and mass to do so popping a shoulder blade while it does ruin some meat will make the deer want to lay down faster, once they do so the adrenalin levels drop and they usually will go into shock and expire soon after.


 
45 or 50, Don't mess around. There are some who use smaller calibers and claim to make head shots. I am not that good of a hunter or shooter when buck fever kicks in. I have seen does that upon the shot, react like they were just waiting for an excuse to die. I have seen big bucks take more lead than seems reasonable (12 gauge slugs and 30/06) and still had to be trailed across several properties. I have seen wounded deer lost, and don't want to again.


 
What is the minimum caliber you would consider? What is your preferred calibre?

Mine is either a .308 Winchester, or .30-06' Springfield. I have thought about the .270 Winchester, but have not got around to it yet. A friend of mine has used a .243 Winchester, and bags a deer every year, with no drama involved with tracking either. Remember, shot placement is king.

I have never thought about using an air rifle for a deer, but I guess there are guys out there who have cleanly taken game with one...I have watched the videos, and have seen them do it, but I just want the power, so I don't hunt deer with an air rifle. Besides, I don't own an air gun with that kind of power, so I have to go the firearm rout.
 
I think the caliber consideration is secondary to the energy at a distance. A high power .177 will kill a deer with the right shot placement at the right distance all you need to do it punch through the skull at just the right place. But that is not usually a realistic shot. I believe it's best to treat shot choice on large game as you would for bow hunting and limit head shots to an absolutely sure thing. Therefore, the likelihood is that it wont be a DRT (Dead Right There) shot, but rather you will need to follow a blood trail to find them in most cases. The best shot for that is not only one to a vital area, but one with a complete pass through, giving both an entrance and exit wound to bleed from. And for that, the ballistic energy holds a little more sway than caliber choice.

The minimum I would consider for hogs or deer would be 300 ft lbs, but I would be more comfortable taking the shot if I knew there was more than that on tap unless I was very close. My state (GA) went with a minimum of .30, but I could not find any that had what I was comfortable with in the power range I wanted. Due to my specific hunting conditions - spot stalking in thick swamp cover - portability and maneuverability were also prime considerations, so I went with the Texan .457 Carbine CF. If your conditions permit, a longer barrel would be better due to the energy it helps produce. The minimum I would consider would be .357. My favorite is a mute point since I have not personally used anything for large game other than the .457. But with that, I can tell you it will flip a coyote over backwards with a center chest shot at 35 yards.
 
If you like to bow hunt, you also likely enjoy tracking to an extent. I would say air rifles would be in that department. Personally I prefer a quick clean kill, dropped in their tracks. .243 with Federal premium nosler partition 100gr. base of neck placement. And yes, the caliber bullet combination does matter. The same Fed. Prem. Nosler partition in .308 doesn’t produce the same effect. I use defense rounds for expansion in .308. The .243 in that round produces major hydrostatic shock that can be seen in the pie sized blister on the inner hide at exit wound. That is, a great amount of energy is transferred to the deer. You won’t see that with an air rifle. Shot placement is always important in everything and practice every angle.