I have done several ballistic gel tests at various yardages and power levels with multiple medium weight slugs (125-175 grain) and found that the .357 hollow point will get plenty enough penetration to pass through the hide, a rib, and most of both lungs. This level of penetration would happen within (and far past) what most think of as "ethical" airgun hunting distances on deer.
With big hollow pointed rounds, they definitely expend their energy quickly so two holes are unlikely (just as with some powder burners) and blood trails can be sparse. So if you are looking for good blood trails, I would suggest using a reasonably heavy, super accurate, semi-wadcutter slug that produces two holes in a deer versus using a hollow point slug that turns into a flat ashtray within three inches of penetration and doesn't have enough momentum to penetrate the offside ribs and hide.
Based on my testing, the .357 140 grain solid semi-wadcutter gives a full pass through on two 15" long blocks of ballistics gel (30"+ and bouncing around upon exit) at 10 yards, impacting around 875 fps. This will give you the very best penetration to produce two clean and open holes even at extended ranges on any size whitetail deer.