I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 20 M church, civil, census, etc for MOST Irish counties. Records before 1863 are increasingly sparse and almost non-existant before 1800.
For Ca(therine) Tigh B 1780 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 4 records: two in Co. Dublin, one in Co. Kildare, and one in Co. Westmeath. Will leave it to you to visit the database and find the DOB.
For a Ca(therine) Tigh and James (Curley) marriage 1800 +/- 5 yrs, somewhere in Ireland, I found 0 records.