For Florence Sullivan B 1845 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 5 rcds: 1841 CRK, 1842 CRK, 1844 CRK, 1846 TIP, & 1846 CRK. Father's forenames for this batch are Florence, John, Cornelius, Timothy, and Michael respectively.
By a process of elimination, I found B rcds for Florence (B 1844) and Patrick (B 1840) with a father named Cornelius in Youghal parish, Co. Cork. Also, there is a Michael (B 1829) with the same father in Youghal. These are close enough individually, even more so collectively, to be for your ancestors - but, no guarantees. A view of the detailed rcds (fees apply) should show whether they have the same mother's name. If so, your chances are even better.