In Ontario it can be shot by the landowner, a direct relative of the land owner or a licenced property protection agent.
It isn't legal to have a friend come over and shoot them.
There are tricks to get a beaver moving during the day, I have solved many beaver issues with a rifle, broad daylight.
The Ontario MNR words it "kill, capture or harass", to the right individual.
Matter of fact, a landowner can dispatch ("kill capture or harass") any nuisance wildlife, with the exception of whitetail deer (special permit needed), and the trapping of black bear. This includes protected animals as well, caution should be used dealing with species at risk (i.e. VTEE List species). Migratory birds require authorization from the Canadian Wildlife Service.
I have owned a nuisance wildlife control company for a very long time, I am also a licenced property protection agent for the MNR. I have seen some crazy stuff that people do to protect their property from nuisance wildlife, one that stands out is a trick the homing pigeon guys use to dispatch hawks..
The landowner has a tremendous amout of rights, so does his immediate family, but to bring in anyone else to do the shooting is poaching. I could care a less what you guys do, but it seems some guys don't understand our regulations, I would hate to see a misinformed hunter lose his rights over a mistake.
*edit* Almost forgot to answer the original question.. A .204 is my first choice.