We used rifles, but we were young and dumb. 12 ga, 3" mag turkey loads would take care of them out to 40 yards or so...
i'm not so sure about using a shotgun. i absolutely drilled a beaver w/ a 3 1/2" hevi-shot shell w/ an extra full choke and that s.o.g. rolled once and never popped back up. they don't expose very much of their body, just their greasy head. i'm using a .223 now!
as always, thanks for the replies!
we began trapping and shooting beavers last year, but haven't seemed to slow 'em down.
to date, we have 5 confirmed kills (2 trapped, 3 shot).
it is too difficult being a "weekend trapper", so i've contacted a couple local trappers to remedy the problem. i'm planning to spend a considerable amount of time eradication all willow trees this spring to, hopefully, dissuade the fury lil' devils from ever coming back.