How sure are you that William & Mary married in Ireland? I searched the Irish statutory marriage records from 1850 to 1885 but did not find a marriage for them. I have assumed they were not RC. Is that correct?
There is one marriage between a William Todd & Mary Bruce in Scotland in the period 1855 – 1878, in Hamilton in 1875. (That’s an area that lots of people from Ireland went to work).
William’s marriage to Rachael Bruce in 1878 gives her surname as Keith so I assume she had been married before. It’s in the Scotlandspeople indexes for St Giles parish GROS ref 685/4 137. Scottish marriage certificates normally list both parents and also say whether each parent was alive or dead at that date, so if you view Rachel’s marriage certificate it should resolve William’s parents names and provide a bit more information eg his father’s occupation.
Let us know what the parents names were, whether they were alive in 1878 and what William’s father’s occupation was, and I’ll see if I can find anything in the records for Armagh.