I have record of a Catherine Ronayne, born March 1840 at Greenhill, Mourneabbey, Mallow, Co. Cork. Pronounced locally in the Mallow area as "Ronan", this Catherine was a sister of my the elder sister of my great grandfather. I have no record of her other than this.
For your relation, do you know if she married Jame Fahey in Ireland? Do you know where their children were born? If you do, then you stand a very good chance of being able to trace her birth or baptism records. From there you will find her parents!
In the middle 1800's, the spelling "Ronan" was most common in Co. Wexford (circa 55 families), then Cork(31), Kilkenny(25), Clare(23), Galway(18), Mayo(14) and so on. I have found that the spelling of the name, even the written records (Birth, Baptism & Marriage) for a single family varies considerably (i.e. Ronayne, Ronan, Ronane, O'Ronain & Ronayn).