They were in Pittsburgh by 1862 according to Robert Sr's death, the 1870 census, and daughter Martha's death record.
Robert Stevenson Sr, husband of Mary Isabella Barclay, was a "minister of the gospel" according to his death record, and 1870 census. Do you know what denomination? Do you know in what church/denomination they were married? This will help greatly when looking for Irish records.
Or have you been through that already?
Or are you looking for the US records?
edited to add:
they arrived between
1) son Joseph's birth in Ireland, which was 1858 on the 1870 census and 12 Oct 1857 on his death record
and
2) son Robert's birth, 1862, according to the census.