Hi zanniesmom! Any luck? Still seeing kitty around? I'm sorry I didn't see this post earlier! But hopefully I can still be a little bit of help.
Some Humane Societies, if they lend you the trap, do so because you have to bring the cat back there. Others will rent the traps. You can also try calling several local vets to see if any of them have a trap you can rent or borrow. They're easy to use, and we have some very helpful trapping hints in this thread: Helping Ferals...
As Hedi pointed out, the best thing to do is to trap this kitty, have him/her spayed or neutered, vaccinated - and if you can afford it, groomed. Ask the vet to put a little notch in her ear. This will signify to anybody who is involved with ferals that he/she has been sterilized. If you're able to do all of this on your own (Kudos to you for wanting to!!!!), you should also ask the vet to use disolving stitches because the cat is going to be returned and released.
If it is a female, it really is best to board her at the vet for a day or two to ensure she's OK and the incision has started to heal a little bit before she's returned.
After that - you can continue feeding her (make sure she has access to water too) - and over time, she may very well come to trust you, and you'll essentially have yourself an "outdoor" kitty - and he/she may even come to want to be petted. With ferals, the best thing to do is simply ignore them. To be near them while eating but not approach them is the best way to gain their trust over time. And don't try to reach out to pet kitty - when they're ready, they'll come up and bump their head on your foot or leg or something.
But all of that is only if you want to put that much work into it. Kitty has survived this long on its own - simply having it sterilized & vaccinated and returning it will help prevent more homeless kitties. Feeding and providing her water may some day turn her into your friend.
I've found working with ferals to be an amazing and wonderful thing. When we release them, a few have run away never to return. Most come back for the food. Many come back and approach us when they need medical attention. If it's a male, he'll stop wandering (looking for females) and make the area around your home his territory if you keep feeding him. If he goes on an excursion for a day or two, it's AMAZING how much you can miss them and worry about them!
Please also take a quick look at this thread about how much vets can potential help in situations like this: Vets are often an overlooked resource!
I think it's wonderful that you have such a big heart to want to help this kitty.
If you want to search for others who may be able to help you, clicking on the Rescue Resources in my signature line takes you to sites where you can search for no-kill shelters or other rescue groups.
Also, if you want to locate low-cost spay/neuter services that may exist near you, try clicking on that link in my signature line.
No matter what you do, I'm wishing you lots of luck! And please provide updates if you get a chance!