The census index at
www.scotlandspeople.gov.uk lists the family as James S Co
nnolly, 41; Isabella, 35; Isabella, 9; and James, 7. If you go to the Scotland's People (SP) web site you can view the original of the census, which will tell you his occupation and where they were all born.
The SP index to the old parish registers lists the baptisms of Isabella on 19 July 1851 and James on 19 March 1854, children of James Smith Co
nally and Isabella McVie. You can view the original baptism records on the SP web site.
James and Isabella were married in Edinburgh in 1845, and the marriage is recorded in both St Cuthbert's parish and Canongate parish, indicating that they lived in different parishes at the time of their marriage. You can view the original marriage records on the SP web site.
The 1851 census transcription at
https://www.freecen.org.uk/cgi/search.pl lists at 459 Lawnmarket James S Connolly, 31, printer compositor manager, born Lasswade, and his wife Isabella, 27, born Canongate. You can view the original census at SP.
On the deaths index, Isabella Connolly, other surname McVie, mother's maiden surname Hamilton, died in St Giles in 1861, aged 35. Her death certificate will tell you the full names of both her parents.
The 1871 census index lists in Newington James Con
nelly, 51; Maria, 40; James, 17; and Walter P, 6. From the IGI at Familysearch, Walter Philip Connolly was born on 12 August 1864 in Edinburgh to James Smith Connolly and Maria Rutherford, who were married on 15 January 1863 in Edinburgh. You can view their marriage certificate and Walter's birth certificate at SP (the marriage is indexed as J S Connolly.)
James Smith Connolly, aged 54, died in Newington in 1874. You can view his death certificate at SP. It will tell you the full names of both his parents, including his mother's maiden surname.
If, as you say, you were 'looking for' James Smith Connolly, you must have been looking in the wrong places.
Everything you wanted to know is available at Scotland's People.
