I was formally diagnosed in the past with an autism spectrum disorder, although I am high-functioning. Now I am beginning to suspect I also carry symptoms of schizoid personality disorder, although this would be a self-diagnosis.
I have never liked interacting with people. This is less of a problem stemming from a lack of social skills than a lack of interest in anyone in my vicinity who could be a social target, and I don't think there's a pill one can take to make other people interesting to one's psyche in perpetuity. It's not a thing for people to criticize what others are interested in, like picking gardening over weightlifting, so I never understood why not being interested in human interaction was any different. That is what being myself feels like. Of course, because interacting with humans is necessary due to how humans underpin critical services like healthcare, there are downsides to not wanting to interact with humans. Despite this, I feel happier alone.
When my family gets close to disowning me outright or people I used to know told me I'm weird to my face, somehow I always come out the other end unfazed, as if I had come to expect it all along and didn't care that I had lost another social link. If someone isn't going to accept that I don't care about socializing with them (and maybe can't, at a neurological level), then there's nothing more I can do.
The fact is, I don't know what else I could do except subjecting myself to what amounts to propaganda (if not therapeutic propaganda) in an effort to convince me I'm something I'm not, for the ultimate outcome of a higher quality of life, regarding a life that is no longer mine. Study authors feel the need to separate people like me out from the average population, as if the condition is an inbuilt part of us. Maybe I have to accept that my brain is different, and not in a way that happens to be more socially acceptable like not identifying as heterosexual. At least in that domain the issue concerns which kinds of people you're interested in, not whether or not you're interested in humanity at all. I have become disillusioned too many times from subversive messaging from individuals who advertise themselves in that way, accepting "everyone", whereas while I tilt my head up and down in superficial understanding in their direction, I can only ever wonder what they're selling.
Also, therapy has never worked for me, the simplest reason being that I don't care about building a relationship with a therapist, especially with the knowledge that the relationship is based on my ability to pay the other party. Nobody I've ever met has understood this, and I have begun to get incredibly suspicious when someone recommends me to start therapy for the 14th time regardless (or even in spite of my own protests), as if it were their off-hand token of sympathy for anyone that matches my general profile.
At the same time I can recognize that the people offering those tokens are not trained to deal with me. Even so, my last therapist said that she couldn't address my concerns because she "was only human."
To answer your original question, I cope with the loneliness that does occur by not recognizing it as loneliness. It isn't advice for you, because my belief is that this is just the pathology of my supposed disorder, and not something that arrived from any personal train of thought. From reading the literature (R.D. Laing, etc.), some believe that the schizoid condition (not necessarily yours, I'm only mentioning this in case it's somehow enlightening) is a contradictory struggle of wanting acceptance from others while rejecting excessive influence and expectations.
I treat the idea of "friends" as "eternal vacation wherever I feel like." They would be nice to have if things worked out, but they don't, so I have to be content living without them. But the problem with the word "friend" is its usage is too vague in my mind. It doesn't encapsulate the expectations the person places on you, which I want none of. It doesn't specify what gated requirements are needed to prevent the relationship from imploding for a reason you interpret as petty or part of a social contagion you do not believe in. As a result, I am not interested in what a neurotypical would refer to when they say the word "friend". My social interest, if any, would be about something else entirely, but which encapsulates the same need for contact/acceptance which is gotten at.
I'm not sure if any of that is helpful. It feels like I'm just venting myself without addressing the question. I seem to have a sort of protagonist syndrome, owing to the "disordered artist" stereotype that is perpetuated, and that fear of being outed as an "I am special"-type prevents me from talking about this earnestly with anyone in real life, especially not on the internet under a recognizable handle. Then again, I don't expect to maintain a vulnerable relationship for the rest of my life at this point, and I'm not even 30.