Looking for information about the parents of the following couple

Heather,

The forenames Ann, Agnes & Nancy are all interchangeable in Ireland (and in Scotland in my experience). So finding Ann mentioned as Agnes is not uncommon.

Death registration didn’t start in Ireland till 1864 so if Mary Ann Colligan/Cooligan died between 1844 and 1851 as seems likely, then there won’t be a statutory record of it.  Assuming she was brought up RC, few parishes kept burial records, so there is often no record of deaths in those records either.  Unusually Aghaderg did keep burial records but she doesn’t appear to be in them. Nor does either Francis.  Of course death registration didn’t start in Scotland till 1855 so if she died in Scotland in say 1850 you face the same problem, a lack of RC records.  Unless there’s a gravestone somewhere there are probably no records or memorial for her death.

Aghaderg RC only has baptism & marriage records starting in 1816 so if Ann was born there before that there will be no record of it. Many RC parishes records don’t start till the 1820s, so there’s a strong chance there’s no record of it. 

I suspect that both Francis Colligan and Francis Hale/Hall died before 1864 and that’s largely why there is no record of them.

I looked at the surname Shannon in Co Down in the 1901 census. There were 288. Only a handful were RC. Most were Presbyterian or some other Protestant denomination. So statistically if she married a Shannon then he’d likely have been protestant, and that would account for Esther being baptised in Killinchy Presbyterian church, assuming it’s the correct Esther Shannon.   The problem with many protestant records is that they are not on-line, so you need to go to PRONI to look them up. You also need some idea of where they lived, though it sounds as though you know that. 

So was Ann born RC, but c 1834 she married a Presbyterian who had died by August 1843 when she married again to William? RosDavies has the 1843 marriage on her site (it’s Cooligan in the Aghaderg register):

http://freepages.rootsweb.com/~rosdavies/genealogy/SURNAMES/C/CooCop.htm

An RC marrying a Presbyterian around 1834 would have married in the Church of Ireland.  Aghaderg Church of Ireland marriage records start in 1814. Copy in PRONI. There was also a church in Scarva but unfortunately its records for that period were lost in the 1922 fire in Dublin.

Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.

The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price.  http://www.nifhs.org (Go to DNA project on the website).