If Mary Stuart was born in Ireland in 1839 there will be no birth certificate for her (civil registration of births began 1864) nor a marriage certificate for her parents (civil registration of Catholic marriages 1864, Protestant marriages 1845). First complete Irish census is 1901
but some fragments for 1851 County Antrim census survive and are available on several online sites. (just realised this is Co. Armagh not Co. Antrim- sorry for the mistake)
Did Mary (Stuart) McGuigan die in Scotland? If so, her death certificate might give some clues.
Have you checked Scottish census records, etc. to see if Mary's parents also moved to Scotland?
Also search on LDS site in case there are any submitted or extracted reocrds there (
www.familysearch.org).