someone else once suggested this and its forever a staple in mine and anyone elses eye....
if the dog wont bite if you catch it and tether it. dont chase it off CATCH it.
put it on a leash and chain, hide it in the backyard... SPRAY PAINT a big old RED X (previous poster did a bullseye, but since you can't shoot the dog - maybe she'll still get the message) on its side. (take pictures before this though and after) OR just take some koolaid or food color (red is better but whatever color) and fill the dogs coat with it - make sure it all dries good before you let the dog go. This way the owner can't just wash it off, and ask the other neighbors if they've seen the "marked dog" ....you've got you a solid case that you've got the right identity.
Make sure you research and CALL the county and the STATE on laws for dogs at large, and harassing/killing livestock. call animal control.
if you cant catch the dog by hand - get the biggest cage you can find. if anything make one, google "humane homemade dog traps" easiest way to do one is make you a large cube/rectangle out of wood. then make you a another square/rectangle the same shape as one of the ends. wire it in with 2X4 welded wire(buy a single large piece of cattle panel should do you, about 20$ at a feedstore)., the extra square - wire it, and buy you a set of hinges. hinge the 2nd square as a door, then buy you one of those touchy gate locks
http://hardware.hardwarestore.com/28-446-gate-parts/automatic-gate-latch-509220.aspx (like this, they come cheaper - shop online or local hardware store) you will have to fiddle with your dimensions so that the latch will catch automatically on the end of the box.
Take a stick thats just sturdy enough to hold up your door, and tie a string to it, on the other end of the string place it over the top of the cage and into the wire so its "inside the box" tie a rock and a piece of spoiling meat on the end (or anything aromatic - pop a few holes in a can of salmon you buy off the shelf at
wal-mart/food store and tie to it) this way when the dog goes in the trap and pulls on the "bait" the heavy door drops down and the auto gate latch should catch, locking the dog in. you're going to spend 60-100$ either on a new dog trap or building your own.