Thank you for the clarification.
Ok, so now we have a birth year of c1841 for Rose Ann and both parents names.
The earliest baptismal records start in 1835 for 2nd Ahoghill and marriages begin in 1836, so there is a possibility, if her family had association with the church she married in, her birth may have been recorded there too - her birth is too early for Civil Registration in Ireland.
These church records would be available to search on microfilm at PRONI or a film could possibly be ordered in by you at a LDS centre if you live near one.
Slight problem arises, though, in that you say now Rose Ann Gailey's father was a William Gailey, yet the Rose Ann Gailey who married James Tippen, apparently, according to earlier posts above, had father James (albeit names on death certificates are only as good as the knowledge of the person giving them, and mistakes are not unusual).