Frankly, the records you are looking for may just not be available anywhere- online or offline. Ireland was part of the U.K. so no records were kept of people travelling between Ireland and Scotland.
1)
James J. Mulholland... birth 1733 Ballygawley, emigration 1750?, marriage 1777 Massachusetts
- Civil registration of birth started 1864 so you need to see if church records survive. See here for microfilmed church records that PRONI, Belfast holds (this will give a very good indication of what might be available)-
https://www.nidirect.gov.uk/publications/proni-guide-church-records (Ballygawley Presbyterian baptisms & marriages start 1842) Most Presbyterian churches didn't, and don't, keep burial records. Also worth checking Church of Ireland for burials as many Presbyterian families would have had plots there. However, some COI burial registers didn't record Presbyterians.
- rather early also for passenger lists. Some
may survive in U.S. archives. Leaving Ireland they might have gone into Boston or perhaps even via Canada.
- Massachusetts records are excellent- try Family Search to see if Worcester marriages for that period are online
2) John Mulholland …birth c1734 Belfast, emigration c1805, children born 1750s
- Belfast probably even more difficult to search as it may refer to what was then the. There are so many Presbyterian churches in Belfast city, is now the city, or indeed an area near Belfast (see PRONI Guide to Church Records linked above to get an idea of how many and what exists as far as records. Also bear in mind that marriages usually take place in the bride's church so they could have gotten married at the church of another denomination or further from Belfast.
A number of the links for this topic are no longer working.
Not sure what links you mean since you haven't posted any.
Added- the tile of this thread is
Paris Records Lookup... If you mean Parish then be aware that only Catholic and Church of Ireland use a parish system. Presbyterian churches are grouped into Presbyteries. Also, there are different branches of Presbyterianism and different Presbyteries and they didn't always attend the church nearest to where they lived.
