It is more common that you're saying 'A day OF May' or 'A day IN May' with this saying? The latter of this was accepted for an answer so I'm curious what would be the more common answer.
Usually you say "O zi de mai" (a day of May) when you describe the day; for example, you say "Este o zi frumoasa de mai" (It is a beautiful day OF May) or "Este o zi rece de mai" (It is a cold day OF May). For something happening in May you use "in", for example "Nunta este intr-o zi in mai" (The wedding is in a day IN May) or "M-am nascut in mai" (I was born in May).
stanealex17 - But " . . . on a day in May" is better "diction" in English translation. And ". . . a day OF May" sounds generally awkward to me without helpful context.
If you mean what would we say in English then, in England at least, I'd say we almost always say a day in May (or any other month) but we might say "a day in the month of May." It would be rare to say a day of May, it sounds odd!. (I was born & raised in England).