I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are sparse.
For Ann(e) Tully B 1842 +/- 2 yrs in Co. Meath, I found 5 B rcds: 3-1842, & 2-1843. One of these may be for your ancestor. A view of each detailed rcd SHOULD show their parents' names. If one of these had a mother's name of Ann, this is partial validation that it is for your ancestor. You decide.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.