Here's some info from a couple of sites which might be helpful:

From Fund for Animals, with a diagram near the bottom of their page:

The best systems for controlling beaver flooding are based on deception and exclusion. The beaver dam can be breached in such a way that the beavers don?t hear the sound of running water, and the water level can then be controlled, unbeknownst to the beavers!

One of the least expensive, easy to install and simplest methods is based on PVC pipes. The beauty of the system is that it is inexpensive ($40?$100) and may take as little as an hour to install. Maintenance is minimal?the pipes should be checked frequently for a few weeks after installation and every few months thereafter. Any debris caught in the pipes usually can be cleared in a matter of minutes.

Before installing any water level control device, be sure to check if your town requires breach permits or has other restrictions.

TOOLS: Saber saw, drill, hammer, sledge hammer, wire cutter, pliers, small rake.
SUPPLIES: At least 4 perforated 6" diameter PVC pipes (10 ft lengths), 2 metal fence posts with holes (longer than the water is deep, plus two 2-ft lengths for cross pieces), a piece of high concrete reinforcement wire mesh (10' long, 5' high, 5" mesh squares), shingle nails, 4 nuts and bolts, form wire.

The system involves putting perforated 10' long PVC pipes (6" diameter, available at plumbing supply stores) through the dam to ensure adequate water flow. You will need to attach 2 or more lengths of pipe together since you want at least 20' of pipe of which 15' is extended away from the dam on the inlet side. The farther the pipe openings are from the dam, the less likely it is that the beavers will associate the pipes with the dam.


from This Site: Nonlethal Prevention and Control

Another method of discouraging beavers is to install a device to manipulate the water level of a pond. This can be accomplished by installing a three-log drain (Figure 3) or wire mesh culvert that the beavers cannot plug. Lowering the water level in the summer encourages wild or planted foods to grow, providing excellent habitat and food for waterfowl.

For more information on constructing water control structures to discourage beavers and enhance waterfowl habitat, contact a Kentucky Department of Fish and Wildlife Resources District biologist or the Cooperative Extension Service.
One innovative way to discourage beavers is the use of a high tensile electric fence (Figure 4). Stake a portable battery or solar-powered charging unit some distance from a run (slide) or a hole knocked into the dam. If you are placing the wire across a slide, mow or trim the vegetation very close to the ground. Finally, string a single strand of wire three inches above the ground or water's surface so the beavers will strike it as they pass through the slide or attempt to repair the hole in the dam. This electric shock acts to repel the animals; if they are shocked enough, they will move to another area.
Daily tearing out dams and removing dam construction materials with dynamite may cause a colony or individual beaver to move. This is very dangerous and not recommended. Even if this procedure is effective, the beavers may move into a new area and become even more troublesome.

Hope this helps; I hate to think of them having to be destroyed.:-)

kat