I highly doubt that Ability Tutor would be ever part of this game in any generation...
Imagine Choice Scarf Articuno throws around Sheer Cold with No Guard...
Or Spiritomb with Wonder Guard.
On the softer side, Drizzle/Drought; Multitype, Magic Guard, Levitating Electric types, etc. Nature Cure would make Status useless...
I doubt they would use anything as ungodly as that, and it's likely they would restrict the Pokemon that could learn each ability, and they might even make it so that some Pokemon cannot be tutored (Slaking and Regigigigigas anybody?)
They'd have to be ungodly stupid to have Wonder Guard able to be tutored.
Here are some I could see tutored without to much hell:
Drizzle (Water types, maybe Dragon or Grass too)
Sand Stream (Rocks, Grounds, and Steels)
Drought (Grounds and Fires)
Snow Warning (Ice only)
Swift Swim (Water types)
Chlorophyll (Grass types)
Air Lock / Cloud 9
Pressure
Guts
Intimidate (maybe)
Pure Power / Huge Power (only to a select few otherwise weak Pokemon. We wouldn't want Huge Power Metagross, but it could work on something like Alakazam)
Torrent / Overgrow / Blaze / Swarm / whatever else (restricted to their respective types)
Stall (might have some use on something other than Sableye)
Things that should definitely not be tutorable:
Speed Boost
Wonder Guard
Magic Guard
Shadow Tag
Anything that gives an immunity (Levitate, Volt Absorb, etc. Dry Skin might be an exception, since it has a drawback)
Natural Cure
Mold Breaker
Multitype
Bad Dreams
Slow Start and Traut (obv)
No Guard
Solid Rock / Filter