Mike B,
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:
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
You haven’t said what denomination the family was, but from the surnames I’d guess probably Church of Ireland (Anglican). I looked at the 1901 census for Fermanagh. There were 56 Burley/Burleigh etc. All were Church of Ireland or Methodist but there were no Methodist churches in Ireland in the late 1700s and so at that point all would have been Church of Ireland. No Manson households in the county in 1901. (None in Griffiths Valuation for 1862 either). People didn’t travel far when they were courting in the early 1800s so if Elizabeth comes from Enniskillen, there’s a chance that James did too. In any case, tradition was to marry in the bride’s church so that also points to the likelihood of them marrying there. Unfortunately the marriage records c1818 when they likely married, are lost (in the 1922 fire). This is what exists for Enniskillen Church of Ireland. There’s a copy in PRONI:
[Earliest registers destroyed in Dublin]
Extracts of baptisms, 1667-1789, marriages, 1668- 1794, and burials, 1667-1781; burials, 1879-1907 and 1941-50;
vestry minutes, 1731-1920; copy deeds, 1796-9; select vestry minutes, 1871-80; register of
church members, 1871 and 1946-50; preachers’ book, 1895-1928.
Extracts from baptism, marriage and burial registers, 1666-1826.
Printed copy of Old Enniskillen Vestry Book, with extracts of births, marriages and deaths, 1666-c.1797.
Extracts from vestry minutes, 1666-1912, which include some baptism, marriage and burial entries.
A personal visit to PRONI is required to view those records. (When it re-opens). But the chances of finding much about the family are not great.
