How to mention your work in a peer-review? I am a coauthor of a critical paper published in Nature. We showed that a common calculation is not reliable without considering new factors. Obviously, this applied to the majority of research on this specific topic. The paper attracted sudden attention in the literature but no wonder that some authors have not yet heard about it.

I receive numerous peer-review request and in many cases the authors are not aware of the new considerations. They appreciated this suggestion during revision.

I have no intention to promote our paper but my concern is that the editor may consider this as a flaw in my peer-review service by mentioning my own paper again and again. I tried to explain it in the confidential report to the editor but felt it is not appropriate too.
If your paper is a relevant factor, then by all means mention it in peer review. I understand your concern about appropriateness, but in the situation you describe it seems unambiguous to me that you should recommend your own paper. 

If you are worried about it, there is typically a "confidential comments to editor" section where you could note that you're recommending your own paper but it's for a good reason. I wouldn't bother doing so unless, say, you've made four reviews in a row for the same journal and every one of them has the same recommendation.