James was born 1830 in Killearn and Ann, 1829 in Edinburgh and these are the birthplaces shown on the 1871 census for them also. I know they were married 12th Jan 1855 in Glasgow.
Ann died at 185, Calendonia Road, Glasgow, in 1891, her dc confirms that she was Ann married to James Stirling, daughter of Andrew Hood and MaryMcGregor.
They had 5 children that I know of
Mary McGregor Stirling, born 1856, Glasgow (named for Ann's mother)
Robert Stirling born 1857, Killearn
Elizabeth Moir Stirling, born 1859, Strathblane (named for James's mother)
Ann Hood Stirling, born 1861, Row (named for Ann herself)
Janet Stirling, born 1864, Row
Of the children, only Elizabeth and Janet are shown on the 1871 census living with James and Ann, both Scholars and their birthplaces are correct also. Oliver doesn't have any occupation but at 6 he was presumably old enough to be a Scholar also?
I couldn't find Archibald or Elizabeth in the 1881, I don't have the 1861 for James but seems certain from the births of Ann and Janet above that they were living in Row (Dunbartonshire) at this time and as Gadget found Oliver's parents were in Milton (Glasgow).
I did find Archibald in 1841 living at Newton On Ayr with parents and family and this looks like it could be the marriage of Archibald and Elizabeth - Archibald McTaggart and Elizabeth Eaton, 9th Jun 1854, Kilmarnock - IGI extract but no sign on SP (or IGI) of the birth of Christina in c. 1858 in Kilmarnock.