I have shot several beavers with a .22 Hornet, and quite a bunch with a .22 magnum. The hornet is about perfect for the job, deadly without too much fur damage, won't blow the head of a beaver apart and often won't exit on body shots for those up on the shore at longer range. It certainly is deadlier than the .22 rimfire magnum if the shot is less than perfect.
I see you are from Saskatchewan. Be careful where and how you use a centerfire rifle for beaver, If there is an open season for big game ( including spring bears) you can get in trouble using a centerfire for beaver. Trappers may use a rimfire only. I mostly use a .22 win mag rimfire now. A .22 long rifle is inadequate, but the .22 magnum with hollowpoints is much more effective. I have also used a .222 for beaver, but it is just a little too much of a good thing if you want to save the pelts. A buddy used to use FMJ bullets in his .22 magnum, they were wounders even on head shots if the shot was not perfect. He switched to hollow points and instant humane kills were much more frequent. Many people now promote the 17 HMR for beaver shooting. It might work OK, but I have trouble trusting that tiny bullet to do the job on such a big critter. Good luck beaver hunting!