Usung the IGI (
www.familysearch.org) method that Nell gave above, it shows that most of this family were registered with the surname spelled as Con. Only the youngest two out of nine are spelled as Conn.
On using ScotlandsPeople, if there are variations of spelling, then the use of wildcards has to be considered. For this case Con* would find the children, plus many more I guess. Assuming the spellings on ScotlandsPeople to be as on the IGI, then use that spelling to reduce the number of wrong results.
The census result for Greenock is more likely to say Renfrewshire than Renfrew Street. On the censuses, the birthplace should be a town, village or area and the county (if in Scotland). The level of detail on a Scottish census form for a birthplace outside of Scotland varies. In most cases it is a country only, but in other cases (good for us) the enumerator has entered a place name too.
ADP