Nora,
It’s possibly worth checking the rootsireland site to see if there's any sign of the family, (ie marriage 1837 and children born 1837 to 1848). It’s a subscription site. They have some protestant records. Failing that you could hire a researcher to focus on Armagh records in PRONI. Researchers in the PRONI area: http://sgni.net
There’s a set of records called the tithe applotment records. They list people with land. So mostly farmers. Here are all the McMurdy entries for Co Armagh. It’s not a census, so labourers, servants, lodgers and anyone without land isn’t listed but it’s a pointer as to where the names could be found in the county in the mid 1830s. And if your family were farmers in Armagh, then probably Margaret’s father is one of these men:
McMurdy, Thomas-- Townland: Greenan Year: 1832-Grange-Armagh
McMurdie, Dr. - Townland : Markethill Year: 1834 --Mullaghbrack-Armagh
McMurdie, Dr. - Townland: Cordrummond Year: 1834--Kilclooney-Armagh
McMurdie, Dr. - Townland: Markethill Year: 1834--Kilclooney-Armagh
McMurdie, Robert-County: Down Townland: Ballykeel Year: 1834-Magheralin-Armagh
McMurdie, Robert-County: Down Townland: Drumnaferry Year: 1834-Magheralin-Armagh
So that tells you to start by looking at particular 4 parishes, Grange, Mullaghbrack, Kilclooney & Magheralin. The family from Greenan were Church of Ireland. I know that because they were amongst the marriages I spotted in the statutory records period 1845 – 1850. I would ask your researcher to check both Presbyterian and Church of Ireland records. Not every church has records pre 1845, but many do, so you’ll just have to hope your family attended one whose records survived. Grange Church of Ireland has records from 1780.