Yes you can kill deer at 100 yards, Eric Henderson killed a deer at over 100 yards with his Texan 45cal look on youtube for Adventures Afield and you should be able to find several of his hunting videos, the farthest I have taken a deer was 69 lasered yards with my XP Badger 40cal shooting a Mr. Hollowpoint 180gr slug with a neck shot dropped in her tracks.
Absolutely you can. Hell, 30 years ago I killed a Deer on a buddies' property that had nuisance permits for his crops. I got a big doe at about 65 yards with a .22 Career with Crow Magnum pellets at 65 yards, back of the neck shot, broke the spine, came out her eyeball. Never took a step.
Marty
Short answer: yes, out to 100 or so yards with a broadside chest shot using a .30 PCP air rifle. Unlike with a centerfire deer cartridge, e.g., .243 Winchester and above, you can't use the high shoulder shot to break the shoulders and disrupt the nervous system to drop the deer and stun it while it bleeds out from macerated lungs. You'll want to shoot behind the foreleg and put your slug through the deer's lungs... if you hit the heart or the large vessels that's a bonus. Your deer will likely run until its blood pressure drops enough from the damage to the lungs to where it passes out and then dies... anywhere from 10 to 20 seconds... and if you don't get complete penetration the blood trail will be reduced making it harder to track.
Long answer: choose a larger caliber if you have one. I have a Benjamin Bulldog in .357, and with a full charge of air and the Nosler 147 gr lead HP slugs it's a better choice than the .30 caliber... basically the air rifle equivalent of a .38 Special rifle shooting the same bullets at 850 ft/sec or thereabouts. I'd still limit my shots to within 100 yards, and I'd try the high shoulder shot with such a rifle knowing I'll get penetration into the chest cavity.
Could you use a .22 or .25 PCP or springer? Sure... but you better be close and you better put the pellet where it counts (brain shot). IMO not an ethical choice, unless you're truly in a survival situation and need the meat enough to risk wounding but not killing.