Searching in Ireland is limited when you are looking at such early dates, mostly you are looking as those who stayed. Even Parish records can be spasmodic.
These are resources you can try:
Census substitute 1864 Armagh Griffith Valuationwww.askaoutireland.ie
(try and match up the Parish's of the McLaughlin and Callahan's
I found 116 Callaghans but 0 McLaughlins? could they all have moved from Ireland? I checked two sources both have 0 McLaughlin's.
By the 1901 Census there are 43 McLaughlin's and 291 Callaghan's. www.census.nationalarchives.iewww.rootsireland.ie
is for bmd's but without knowin a parish you might not get the right person but worth checking out as you have both parents names and so should be able to get all their children born in Ireland. It is a not for profit but fee paying website.www.emeraldancestors.com
free to view but pay for records
The british telephone book for northern ireland has
13 Callaghan and 4 McLaughlin's - none same area
I would be writing a letter, photocopying and sending to these folks as stamps are inexpensive genealogy. They maybe able to help with local churches, cemetaries etc. Full addresses and postal codes are provided.