I help many folks in this area with predator control. I don't claim to be an expert in this field. But, I have a blast doing this since my health prevents me from hunting as much as I used to. The more I do this, the better I've gotten. My typical solution is to kill the offending predator. You cannot legally do this with raptors. Defending against birds-of-prey can be a very challenging proposition.
Keeping your birds in enclosures is obviously the best deterrent. But, like you, and many others, I enjoy letting our birds out to forage for a while each day.
Having shrubbery for them to hide under will help. A good observant rooster and even some hens are great at warning the troops when a raptor appears.
To discourage birds-of-prey I've had best success by stringing small monofilament fishing line across the area the birds forage in. I stab pvc pipe and small saplings across the area and string the monofilament in vertical, horizontal and diagonal directions over and across that area. I've had a few neighbors witness the birds hitting the string and getting knocked for a loop. In just about every case it has worked in nearly eliminating raptor damage. Owls seem to get nailed the most by this method. Now, owls are by far the greatest threat from overhead we have here. We also have a crazy amount of hawks but, I think they see the string better and avoid the area. Which is a good thing.
If the government would allow us to capture raptors, there is some very efficient leg-snare methods. However, trying to remove a live hawk or owl from a snare could be some rather hazardous work!!!