Is it a standard sized rooster? i am surprised he's running off for a cooper's hawk. My only rooster that just screams out alerts and then dives for cover is the serama, but, he IS pint sized, so i think it's impressive he even keeps an eye out! I do have trees on the property where they free range though, which helps. I would definitely consider getting a dog, like a great pyrenees. They are supposed to be great with chickens. And they super gorgeous!
All my rooster send up alarms and everyone goes running or my great pyrenees comes running to protect. Three of my rooster stand out in the open (we live in a hollow in the woods) sending up an alarm and putting themselves in harms way until all the hens are hiding. I love real men.