The date of the marriage and the children’s births are all well before the start of statutory registration in Ireland (1864, save for non RC marriages which were registered from 1845 onwards). So you will need to search church records for this marriage and for the children’s baptisms. Do you know what denomination this couple were? Looking at the 1901 Irish census there were 132 people in the country named Loy. All were RC. There were 292 named Calderwood. The vast majority were Presbyterian (so descendants of Scots who settled in Ireland in the 1600s). So my guess is that this was a mixed marriage. Unless one converted to the other’s denomination, they may have married in the Church of Ireland (which would marry any denomination).
Not all parishes have records for the period you are interested in, and not all of the surviving records are on-line. I searched rootsireland but did not find any record of the marriage or baptisms. The most complete collection of records for Ulster is held in PRONI (the public record office) in Belfast. A personal visit is required to view them. However without some idea of where in Tyrone the families lived, there’s a lot of records to search through.
I looked at the 1901 census for Tyrone and there was only 2 Calderwood families living there then. They lived in Tullagh Beg which is in the parish of Donaghenry. I looked in Griffiths Valuation for 1859, and there was only 1 Calderwood family listed in the county then. It was also in Tullagh Beg. Plot 9 a 14 acre farm. If you have no other leads, you could start with the records for that area.
Donaghenry Church of Ireland records start in the 1700s 9with some gaps), and 1st Stewartstown Presbyterian start in 1814. The RC records don’t start till 1861 so if that’s where Margaret originated the records for her baptism won’t exist.
The Tullagh Beg farm today is on the modern Tullaghmore Road, outside Coalisland.
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 are running an Ulster DNA project and can offer FTDNA testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).