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. You obviously need to know the precise denomination 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:
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:
Enniskillen RC’s baptism records don’t start till 1838. Their marriages start in 1818.
Ancestry lists Thomas Coyle’s marriage to Margaret McManus on 8.2.1834 in Enniskillen. Unfortunately I can’t find the marriage in the registers. Presumably it’s there somewhere:
Marriages at that period don’t give you much information. Just the couples names, their 2 witnesses and the date. No parents names or townlands (addresses).
I also see a baptism for a daughter Mary to Thomas & Margaret, on 4.3.1839 in the same parish. Sponsors were William & Margaret McGan… (illegible).
I looked for Patrick & Rose’s marriage but did not find it. Presumably it was before the start of the parish records.
You may struggle to find anything more on this family due to the general lack of records in Ireland for that period.