As noted in just about all threads on this topic, relocation of live predators is not advised and in most states, illegal.
So what do with the coon, possum, etc.., you caught that is alive in your trap?
1. .22 rimfire: A .22 rifle with subsonic shorts or even CB caps is the best way to kill a predator. 1 shot between the eyes is instantaneous. While discharge of firearms is prohibited in most city limits, if done properly, no one outside of 20' from the trap will hear it. To do this, you have to place the muzzle of the rifle within 2" of the animals head before you fire. The skull absorbs the shock wave, muffling the sound. Make sure you the trap is over dirt, not concrete surface and have the gun pointed almost straight down so the bullets enters the dirt if it leaves the skull. Do not use a revolver in urban areas2, the gas escaping around the cylinder will still make a loud crack!
2. High Power Pellet Rifle or Pistol. Yes, a high power .177 or .22 pellet gun, used in the same manner as above, will kill a predator. But you must shoot it point blank and not miss the brain case.
3. Drowning. I have worked in wildlife biology for over 25 years. I don't know of any state regulation that prohibits drowning trapped predators.If someone does know of such a law, please post a link.
Fill a large enough container with water and submerged the entire cage. It will take less than 5 minutes. The critter will struggle for about 1 minute. Its not for the faint of heart but it is fairly quick and you don't have to own or discharge a gun. Beware that the surface of the water is liable to be covered with fleas, might want to have the bug spray handy.
4. Use Conibear traps. If it is legal and there is no chance of catching someones pet, use a conibear trap, which kills instantly. Many states prohibit their use on dry land. The 120 ( a 110 with 2 springs) or 220 is the size used for raccoons and possums. These traps can be dangerous, a 2200 can break your fingers, wrist or arm if you mess up setting it. If you don't know how to use it, ask someone who does to come set them.
If you dont have the ability or cant bring yourself to dispatch a predator, call a critter control company, your local state game commission office or ask a friend who can do it for you. But dont relocate the critter.
1. Double wrap in heavy duty trash bags and place in your trash can.
2. Bury: Bury at least 2' deep to avoid it being dug up or smelling.
Dont just take it and dump somewhere along a road or on someone elses property, that is also illegal in most states and you risk spreading diseases.
1. Predator control is a secondary tool, first step is providing your birds with a lockable coop and a secure 5 sided run where they are as safe as possible, especially at night.
2. A chicken acclimated dog is probably the best protection from mammalian predators you can have.
3. Hawks are another whole topic.
4. Seeing a predator, even coons or possums, during daylight, is itself not a sign of distemper or rabies. Seeing a predator in daylight acting lethargic, stumbling around or otherwise acting sick, is a clear sign of disease. Call animal control and dont go near it, get your pets secured.
Hope this helps.
Please feel free to ask me any questions about trapping and predator control.