I believe that Alberta just changed the hunting regulations this last season to allow air pistols as well
http://www.albertaregulations.ca/huntingregs/genregs.html
GENERAL PROHIBITIONS
It is unlawful to
1. ● apply on draws or obtain recreational licences in Alberta if:
i) your hunting privileges are under a licence suspension/cancellation in Alberta (or elsewhere) or
ii) if you fail to pay your fine after being convicted of a provincial hunting or provincial sportfishing offence.
● carry or use another person's licence or tag or allow another person to use your licence or tag.
2. harass, injure or kill any wildlife with a vehicle, aircraft or boat.
3. hunt any wildlife with or from an aircraft, or communicate, for the purpose of hunting, the signs or whereabouts of wildlife seen during a flight on an aircraft.
4. transport dead wildlife taken by others without an accompanying bill of lading (click here for downloadable pdf ) signed by the licence or permit holder and providing the following details:
* the kind and number of the licence under which the wildlife was killed or possessed,
* a description of the wildlife,
* the points of origin and destination, and
* the date on which the wildlife is to be transported.
5. set out, use or employ any of the following items for the purpose of hunting any wildlife:
* an arrow equipped with an explosive head,
* a firearm that is capable of firing more than one bullet during one pressure of the trigger or a firearm that can be altered to operate as such,
* a light,
* a shotgun of a gauge greater than 10,
* a device designed to deaden the sound of the report of a firearm,
* recorded wildlife calls or sounds, or an electronically operated calling device except; 1) when hunting migratory game birds with the use of calls or sounds that mimic snow geese and the hunting does not occur with the use of decoys that mimic migratory game birds other than snow geese, or 2) using electronic calls can be used to hunt crows, magpies, coyote, red fox and wolf (using sounds that mimic these animals or rodents).
* a pistol or revolver unless
– the person is a licenced trapper (holding a federal authorization) who is dispatching an animal caught in a trap, or
– it is an air powered pistol or revolver that discharges a projectile at less than 500 feet per second (often used for hunting small game).
* live wildlife,
* a swivel set or spring gun, or
* a poisonous substance or an immobilizing drug
And higlighted part contradicts Wildlife Act last time I checked:
Wildlife Act stipulates handguns prohibited for hunting as restricted or prohibs, requiring ATT and a license.