Statutory birth, death and marriage registration (in some jurisdictions called Vital Records) only started in Ireland in 1864, save for non RC marriages which were recorded from 1845 onwards. So you probably won’t find statutory birth, death or marriage certificates in Ireland for this family. For earlier years you usually need to rely on church records, where they exist. Ideally you need to know the precise denomination and have some idea of where the person was born in order to search the correct records. Not all churches have records for that period and not all are on-line.
RC records are mostly on-line on the nli site:
https://www.nli.ie/en/family-history-introduction.aspx
For other denominations, the churches usually hold the originals but there are also copies in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
Lurgybrack is in the parish of Leck. It’s early Church of Ireland (Episcopalian) records were lost in the 1922 fire and it has none for the period you need. It doesn’t have a Presbyterian church so I’d be looking at adjacent parishes ie Aghanunshin, Conwal, Convoy, Raphoe & Raymoghy.
Many churches don’t have records for the late 1700s/early 1800s so it may be hard to find some of this information. The marriage around 1841 might be in the records though.
Tradition was to marry in the bride’s church so a marriage and the subsequent baptism of children are not necessarily in the same church.