I raise parrots (Macaws, Amazons, African grays, Cockatoos, Conures) and chickens. I have been doing this for over 50 years and racoons have been by far the worst predator of all. With the value of parrots I have learned to double wire all of by cages and flights that are located outside. The separation needs to be 6" or greater. When disturbed at night, the parrots will climb up the wire on the sides of their flights and also hang from the roof where the coon can grab them. They will pull off legs and wings before they finally kill the birds. They are butcherous!!! They also work in groups, with some scaring the birds while another one will grab it.
Also under flights I suspend 2 x 4" mesh welded wire well below the bottom of the cage. This not only protects the birds from the coons pulling their legs off through the wire on the floor of their pens (and yes, they can pull legs off through 1" x 1/2" weldend wire) but it also prevents them from getting under the flight or cage and flipping the feed pans over so that they can eat the feed off of the ground. All of my flights and cages are 3' or more off the ground to protect from mice and snakes. The loss of one parrot will buy many rolls of wire. And don't use chicken mess. This is fine for inside the hen house, but not outside. But the parrots will even tear through chicken mesh. But the coons can tear through this is a skinny minute. Only use welded wire or chain link fencing. By using the larger mesh wire under the pens, this allows droppings and spent food to fall to the gound and not collect in the wire.
One can never be too careful. Don't think that just because you have never had a coon problem, that you are exempt. I live in the country, but when I kept some birds at my business in town, I lost any number of them to coons.
And don't think that you can relocate a coon. Carry it 150 miles away and it will be back in 6 weeks. They have the best homing instinct of any known mammal. Put him in the stew pot. I catch all of coons in live traps, so to be humane. And if you don't like coon, just advertise. I have been offered $40 each, but I have never sold one. I give them to someone who thinks coon is food from heaven. If someone likes coon, they will walk ten miles for a coon for supper.
If the game warden only took the owl 4 miles away, it will be back tonight, guaranteed. So be prepared. She is probably feeding a nest of babies. That takes a good chicken or duck a night.