Hi,
One handed crossbows are classed as Prohibited Weapons in Canada.
Full sized hunting crossbows are quite effective and widely used to take big game in Ontario.
I have taken a few grouse with a sling-shot but I never put in the time to practice, I missed many more than I got.
I have seen rabbits and grouse taken with air pistols and rifles, they work well if the game is close and the shot well placed.
Myself I prefer a compact .22 rimfire rifle or short barreled shotgun as they are more accurate and effective, especially at longer range.
Mike