What should I do if a coauthor, who has contributed the most among my coauthors, declined to be listed as a coauthor? For a paper with coauthors, what should I do if one coauthor, who I feel has contributed the most among my coauthors, declined to be listed as a coauthor and wished only to be acknowledged in the acknowledgements? The reason he gave for declining was that he did not think he has contributed significantly. The other coauthors knew this, but didn't say anything.

This happened once in the past, and at that time I did as requested by the coauthor, i.e. I removed his name from the list of authors and acknowledged him instead. The other coauthors still had their names as authors of the paper. I felt uneasy about it because I didn't think that it was right. I mean, if my second author did not think that he had contributed enough, why should the third and fourth authors stay? Of course the reader wouldn't know this, but I knew, and my third and fourth authors knew.

Now I am facing the same situation again.
I have previously asserted that a co-author has the right not to be recognized as a co-author, if that is her preference. If she is amenable to publication (as would appear to be the case here), then you may proceed with publication. (If not, then you would need to remove her contributions entirely, and then see if the paper is still salvageable in that form.)

However, you should make sure you have a written documentation of the coauthor's declining of credit. You should also make sure that you have explained clearly why you feel she should be co-author; perhaps you can include a list of the contributions of the other co-authors.