This post has information about how to trap and dispatch predators on your homestead. If you think all creatures can live in harmony, you should probably skip this one.
After that we started locking the door and letting them out in the morning. We forgot to lock the coop up one night and lost four more chickens for a total of seven dead. I constantly have the trap out and baited but these raccoon's are smart, I think they have been trapped before and let go. Please never do this. Once a raccoon learns what a trap is they will avoid them in the future.
If you find yourself in a situation where the racoon you are trying to trap is avoiding your trap, try to camouflage your trap with just the front open. I am assuming you are using a Havahart trap or something similar. You can cover the trap with a cardboard box and cover that with leaves leaving only the entrance open. Use marshmallows as bait. This will stop you from catching cats with other baits like tuna or meat.
When you are faced with dispatching the animal you trap, you can read about many methods on the best way to do it. I researched them and came back to my initial thought, a single round of .22 LR. The animal is caged and it is easy to get a clean kill with one shot. Other methods are much worse. Some people throw the cage in water and drown the animal, I find this horribly cruel. Some people use car exhaust, basically suffocating the animal. This is unnecessarily cruel. One bullet is the fastest and most effective method in my opinion.
While we are on the topic of dispatching unwanted pests. Some people put out anti-freeze for cats and other unwanted animals to drink. Anti-freeze is sweet and animals will drink it thinking it is food. The main ingredient is ethylene glycol which is naturally sweet. The death these animals face is unbelievably horrible. The people who do this are some of the worse people. Please never do this.You can avoid accidental exposure by making sure the anti-freeze you buy has been treated with denatonium benzoate, a bittering agent added to make it unpalatable. Not all states require it to be added and most repair shops use professional grade coolant which is exempt. Please ask the question when buying anti-freeze or having your car serviced.