Hunting for McFarlands and Murrays

I'll be in Northern Ireland in August and am really hoping to see where my relatives came from.

Looking for help pinpointing information, and suggestions of where to look when I'm in the area.  I plan on being at PRONI the first 2 days then heading to Ulster Folk Park and haven't decided on remaining days.  Help with things to concentrate on at PRONI would be great.

One set of third great-grandparents are really brick walls.   Charles Murray and Jane ?? were from Ireland and left from Sligo in 1824 to New Brunswick on the ship the Elizabeth with their son James (born 1821). Census reports show Charles and Jane born between 1797 and 1802.  So far I haven't been able to find anything on any of those Murray.   Their daughter, Catherine, is married to my 3rd great-grandfather William McFarland/MacFarlane.   Jane's death certificate from Ohio has no details - no parents, no maiden name, etc.  I do have a DNA match to a descendent of Charles, but he hasn't gotten anywhere either.

The Murrays were Church of England.   The McFarlands were Presbyterians in Canada and the US, so guessing they were in Ireland as well. 

I know more about my 3rd and 4th great-grandfathers, but not a lot.

I'm pretty sure the McFarlands/MacFarlanes were from County Tyrone before the family left for New Brunswick, Canada in 1833.   I've found references to Andrew Sr and Andrew Jr in Tithe Applotmment books for 1827 and 1830 - and think they were either from Liscabble in Bodoney Lower (mention of McFarland Mountain) and Ficcary in Cappagh  - but have seen other references to either Gortin or Newtownstewart. 

Andrew Sr was born around 1781 and had a brother King born 1784 and I think a sister Ann who married a Black in New Brunswick.   I don't know who his parents are.   There is a reference to an Andrew McFarland in the UK, Royal Hospital Chelsea Pensioner Soldier Service Records, 1760-1920 that shows birth in Cappaghe, Ireland and discharge in 1833 which is when the family left.  Again - no proof that it's the right Andrew - there are a LOT of them.

Andrew Jr was born in 1815 and has at least 2 brothers - Armour (1811) and William (1818 - my 3rd ggfather)  I found a reference that Andrew and Armour were born in Londonderry and William in Tyrone - but it didn't have sources and I haven't been able to find anything.

Both Andrew Sr and William were married to women named Catherine Murray/Murrey.   I haven't found anything about the older Catherine, but census reports list her birth year as 1781 and possibly from Donegal.  William's Catherine could have been born in 1818 (gravestone) or 1825 which seems more likely because her parent's permission was needed at their marriage in New Brunswick in 1842.

It is possible that the senior Catherine and Charles were brother and sister, but that's just a guess.

Any help would be greatly appreciated!