urgent help needed to trap a cat to bring to vet

I've had a stray living in my backyard the past few years and I suppose we've become attached to each other. At first I thought she might be feral but over a long amount of time she has become a good pal, sometimes even instigating me to pet her. But anything out of the ordinary, any movement, and she's gone for awhile. She's very pretty - I think maybe she used to be abused. And very observant and smart.

She does seem to be spayed, and today she is now sitting outside my back door coughing harshly. But if I go to the outside she runs back. What I need help with is trapping her - any attempt on my part in the past failed. Even if I use food for bait, which she now expects from me at least once a day. What I'd like to do is just get her to a vet, and adpot her fully.

Not to mention that the other night I saw a raccoon in my backyard.

I have tried slope street cats but they are too busy and im worried that if i wait for training it'll be too late - if anyone knows anyone or any service that would help me trap her I'd be willing to pay a fee. Any advice is appreciated.

Thank you.