I’ve spent a lot of my life in pretty much the same state as you describe your friend being in. I feel fortunate that, some years ago, I found someone that I’ve been living happily with ever since.
If by “find a way to make peace with being single”, you mean get to a point where she accepts and is happy with the idea of being single for the rest of her life, I think that’ll never happen. There are people who can be permanently single, and others who just can’t. She sounds like she’s of the latter group, and trying to get her to change that most likely won’t work. Those who have responded on this thread that they’re happy being single, that’s great, more power to ya. But not everyone can be that way, and if someone isn’t then they’re not, period.
Also, a lot of the advice given here: join a club, get a hobby, join a church group, focus on work, etc. are, you’ll have to pardon me for being blunt, just trite. I heard that kind of advice from friends for years and years, and it doesn’t help.
I think the way you can help your friend is not to try to get her to “make peace with being single” but rather to help her to realize that things take time. She’s not going to find a good man RIGHT NOW, it’s just not going to happen. She needs to accept that finding the right person takes time, and it takes work. And it almost certainly requires that she go out with a lot of wrong men. And, unless she gets really lucky, probably requires going through one or more disappointments of thinking she’s found the right man, only to find that he doesn’t think she’s the right woman. None of that is pleasant to hear or think about, but it’s most likely the reality.
What she needs, and what you can help her with, is patience. She has to accept that it’s going to take time, and that jumping into a relationship (or just bed) with the first not-a-total-loser that comes along isn’t going to make her happy in the long run. And if she starts down a path of getting involved with someone that you know she’s just “settling for”, you, as a good friend, may have to take on that thankless task of trying to show her the error of her ways. And as hard as that might be, it may also be the best thing you can do to help her.