Just to avoid any duplication of effort, can you clarify what you are seeking, that is, what do you know and what do you not know?
Are you looking for children of Gerald Convery and Charlotte McVeigh? If so, it's unlikely you will find any official source online, it's just way too modern/recent.
Are you looking for children of James Convery and Mary Dorrian? GRONI online allows you to search for civil birth records which are over 100 years old, the following Convery births registered in Newtownards registration district with mother's maiden name Dorrian / Dorrion are just a possibility and are available to view ("Full" option lets you see the full record, including a digitised extract of the original document for 5 credits, £2 at the time of my post):
- Charles Convery, born 8 April 1912;
- Robert Convery, born 17 April 1913;
- Nancy Convery, born 30 October 1914.
https://geni.nidirect.gov.uk/