When is St. Mary's birthday?

If by "Saint Mary", you are referring to Mary the Mother of Jesus, history does not record the year of her birth. Modern historians place Jesus' birth around the year 4 or 5 BC. For Mary His mother to have been a woman of childbearing age during that period, a plausible range of years for her birth would include the third to fourth decades of the 1st century BC. (20 - 40 BC).