Stevens Model 200
.308 Winchester
Leupold Rifleman 3-9x40 Scope
Total Cost about $650 brand new.
I guarantee that as long as you have that and a nice comfy spot within 100 yards to sit and wait...you will never have a beaver problem again.
These items may be "low end", but they will perform the task at hand VERY well. Have no doubt.
Plus you have a great all around rifle for hunting deer, hogs, black bear, antelope, mountain goats, moose, elk, or pretty much any large game in the United States.