For Esther O'Rourke B 1850 +/- 4 yrs, Kiltoghert RC parish, Co. Leitrim, with the father's forename unknown, I found 1 rcd, 1850. Father's forename is James. This fits your criteria exactly. It is highly likely to be for your ancestor. A view of the detailed B rcd SHOULD show both parent's names.
For James O'Rourke M 1846 +/- 4 yrs, Co. Leitrim, I found:
Church Marriage Ororke James 1842, Manorhamilton Church Marriage Roark James 1844, Fenagh Church Marriage Ororke James 1845, Cloone Church Marriage Roarke James 1845, Manorhamilton Church Marriage Rourke James 1845, Cloone Church Marriage Roark James 1847, Kiltubrid Church Marriage Ororke James 1849, Manorhamilton
One of these MAY be for your ancestor. You will need to see whether one of these M rcds shows the bride's name found on Esther's B rcd.