Live-trapping raccoons and oppossums easy and usually followed by dispatching. Enables release of non-targets. Traps easy to acquire and can target wider array.I concur w/ the Dukes can trap.
On that note, do yourself a favor and dispatch any trapped critters.
If you're going to spend the time, effort, and $$$ live trapping and relocating, you might as well make a TV show about it. You're not doing any favors per se by relocating. Once a predator has the taste for your chickens, he'll either be back at your coop looking for handouts or will simply find the nearest other chicken owner to menace.