My collaborator has asked to be only acknowledged in a paper. Should I make him a co-author?
The answer depends on how firmly Y has declined authorship.  I don't think it's appropriate to ask the referees to decide on authorship. 


You cannot list Y as an author without his consent.  If he has firmly refused to be an author, that is the end of it.
If Y has simply indicated that acknowledgment is a sufficient form of credit, but left the door open to being an author then it's up to you.  I have responded in this way sometimes when I felt my contribution was sufficient for authorship but I didn't want to step on anybody's toes.  I try to err on the side of being generous with credit, so I would say to him 



  "I feel that your contribution warrants authorship.  Are you willing to be listed as an author?"


If he still says no, then just acknowledge him.  You can include the statement of how critical his part was in the acknowledgment.

In the comments, there is a suggestion to state in the paper that Y has declined authorship.  I don't think this is wise; it needlessly draws attention and may make people speculate as to why.  If I were Y I would not want that statement in the paper.