I have trapped several beavers using a leg hold trap. I always use a drown set with two #2 traps. Wire a two pound flat rock to the bottom of the traps and set them in the water. Secure the traps with a length of wire, like phone wire or something and give it enough slack to let the beaver swim to deep water - that is safety to them. When he reaches the end of the wire he keeps swimming but doesn't realize he is getting nowhere. The rocks eventually tire him out and he drowns - never fails.
Set the traps either where there is a well worn run where he comes out of the water a lot, visualize the length of the beaver, swimming up to shore and then putting his hind feet down to climb out. That is where you want to place the traps. I place them side by side, with one a little farther out than the other. You can also place some tender aspen branches, just a few tender ends, in the bank where he has to climb up to get them. Aspen is their favorite. If you can find his underwater hole you can also place the traps at the entrance to the hole. When they swin into the hole they put their hind feet down to give a push up the the shaft to theen.
Good luck.
that sounds like a great way! Where are you getting the aspen branches?
Sounds like you might be from further west? The cotton wood leaves are bigger but similar?