Quote:
I posted you a link to 
petsmart that carries several repellant at relatively low cost. Some work, some do not. Other than securing your coop so nothing can get in, it's all going to be hit or miss. I just lost several in the past month to something, i am not handy at all when it comes to construction, we were to rebuild my coop to make it more secure but things happened and the time was just not as it was supposed to be with my husbands last visit home. I quickly masterminded a temporary secure shelter for them and so far so good. I'm still not 100% relaxed, but i'm better.  I even reassembled my peep pen inside the run for my 2 babies yesterday, it was NOT penetrated by the intruder any of the 3 times it came around and yet I still for the past 2 nights cant bring myself to leave the babies out for the night
You say it's secure, and yet it really is not if it is not fully enclosed where others can "visit" and the birds can get out on their own accord.  If you pen them up for the night you might just have to learn to wake up earlier than 8,9 or 10am. Get up, let them out and go back to bed if need be, or leave them in untill you wake up naturally. Chickens, I have found will not attack you for making them stay penned up until 7 or so. Even if they're used to being let out between 530 and 6am. I slept in once and i survived, and so did they. I have a waterer in their coop so they arent dieing of thirst until i get out in the morning.  
You said you dont have raccoons or other predators where you are, but you being where you are, you have a TON of predators that will get your birds!!!!! Here is a list I found with a simple google search of those in your neck of the woods. MANY of them will climb a fence to get what they want. I honestly do not seeing a simple domesticated house cat going in and attacking your chickens all the time. Like i said in my last post, all these people saying kill it???? Makes me question their compassion for any animal. ESPECIALLY those who say to torture it by drowing etc... if it's that much of an issue and you are certain its the cat doing it, catch it and carry it to the shelter or call a feral cat rescue in the area. There are tons out there. Forget the neighbor at this point, they are useless IMO and don't care about not only your animals but their own. Maybe its not their cat? Maybe it adopted them and they didnt fully agree to taking him on? I dont know but do what you think you need to do, but do it informed and fully aware that just because you rid yourself of this cat, your set up as you describe is not ideal for an area with Bobcats, Coyotes, Badgers, snakes, lizards, and hawks. Saw a redtail hawk carry a rabbit off from our field that was bigger than one of my dogs one day. Do not underestimate the abilities of ANY predator and good luck!
Mammalian Predators
Badger
Bobcat
Coyote
Kit Fox
Mountain Lion
Ringtail Cat
Reptilian Predators
Snakes and Lizards 
Mojave Rattlesnake
Black-collared Lizard
Mountain Kingsnake
Avian PredatorsRaptors and other Birds 
Red-Tailed Hawk
Golden Eagle
Great Horned Owl
Barn Owl
Roadrunner
Raven