The best way to get rid of them is to remove the food source. There are a few problem with shooting them, even beyond the legal issues.
For one, it's very common to believe that the hawk you see is the one doing the killing. That's basically how redtails got the misnomer "chicken hawk" in the first place. A coopers hawk hunts by stealth, and sneaks in and kills a chicken. Farmer hears a ruckus, and looks out to see the redtail carving circles in the sky...
If it is actually a redtail doing the killing, is it just one? Or one of a pair? Is just one doing the killing, or are both?
You're in an area that ends up with a lot of birds at this time of year, due to the migration. They're all doing their best to survive, in a tough world (65% of redtails die before they reach one year of age, on average, only 5% make it to 5 years old, and they don't breed until they're 3 years old). To survive, they need food and habitat. Apparently, your yard offers something they need. If it didn't, they wouldn't be interested in it.
If you kill the hawk, what's to stop another one from being attracted to the easy food source?
Trapping and relocating is unlikely to work. I've trapped a LOT of hawks, and even some falcons (I'm licensed). If you don't know what you're doing, you'll probably fail, or injure the bird, or break feathers (which could easily sentence it to death). If you do succeed, and don't wreck the bird, how far away do you intend to move it? What stops it from coming back? Keep in mind, it may just be visiting your area after a flight from as far away as Canada. Moving it a county or two away isn't a big obstacle for it... Especially if the food is good at your place. If it does stay away, we're back to the question of what stops another from moving in?
Dealing with wildlife causing problems with domestic animals is nothing new. Predators have been shot, trapped, poisoned, etc, for a LONG time. It's proven itself to be ineffective until the overall population is reduced, not just the currently-offending individual. I live in the country. I have chickens and ducks, pigeons and hawks. The local hawks have sometimes killed my critters. It's a small price to pay, IMO, to live as I do. I choose to protect my critters from predators, rather than remove the predators.
Locking your chickens up, thereby removing the food source, is really the best long-term option. How many do you have? Do they need to free-range? If so, have you seen the "drag" cages used for producing meat-chickens on non-commercial levels? Basically they're an 8x12ft bottomless cage about 2 feet tall. Keep the chickens in it, and just drag it over a few feet each day, to give them fresh ground. The water dishes can hang from chains inside. The chickens are protected, but still get benefits not offered by keeping them cooped. Letting them run loose is really just an attractive nuisance. What self-respecting predator would pass them up? How could they know they weren't supposed to eat them?
