Hi FamilyHistorian60,
I'm not from the area but I live in Co. Galway - the other side of Lough Corrib, in KIllursa parish. See map for connections between Ballinakill, Carraroe and Killursa(distance reference).
You're probably aware that civil registration in Ireland started in the 1860s for most (marriages for non-catholics started in 1845) - see link, though there are earlier church records available (along with civil records) online. You can access the Catholic Parish Registers online at the National Library Website.
I'm guessing they married at Carraroe (Bride's parish). If you have more details about their marriage or birth of their children (townland they were born in or lived in, dates eg) I might be able to help make the connection with the correct family. I will look through the Ballinakill records to see if I can find baptisms but you don't say where the children were born so I could be looking in the wrong parish records.
Because many of the census and other records were destroyed 100 years ago you may not get census information until 1901 (assuming they still lived in Ireland at that time). You may be lucky to find old census details from before 1901, though they are rare.
Either way, more details of events (birth, marriage, death) along with location (townland, County), dates (even rough estimates), etc can help me or others to find connected information for you.
Regards,
Tim (Killursa Parish).