I searched the Irish Family History Foundation's database. It contains 11,500,000 surviving rcds for abt 60% of Irish counties. Abt the same number of rcds remain to be digitized. Rcds B4 1840, both digitized and undigitized, are sparse.
For the Rourk (+variants) surname, the earliest B rcd is for 1721, the earliest M rcd 1752. There is only a SLIM possibility that the digitization of more rcds will extend this range further back in time to cover your era of interest.
Suggest you google the Foundation's name to lead you to the database. Register, opt to be notified as rcds are added, and browse the database (free).