Hi journeyman
If you are willing to spend a relatively small amount of cash, you can search online for the death certificate of Cornelius and/or his wife. For an extra amount you can download (I think about $20AU) an image of the certificate. Australian certificates usually (IF the informant knew the detail) will tell you the number and/or ages of living children, names of parents and time spent in Australia. Family history centres may have free access to CD indexes, but there is no free access to the full certificates. The downloads are the cheapest access for Victorian data. To find any living descendants you may have to track deaths of the children of Cornelius. The link is 3 lines long. If you go here
http://www.dvc.vic.gov.au/bdm.htm and then track through the BDM registry, you will find details & access to the records.
The other options are via cemetery records and/or newspapers, which are not so easy to find online.
If you check the oz white pages
http://www.whitepages.com.authere are about 8 Coughlans listed in the Ballarat area. Whether they are any relation? Could be worth a snail mail.
There is also a Ballarat genealogical Society
http://www.ballaratgenealogy.org.au/ with a multitude of links and historical information. They have an interesting collection of indexes for sale - perhaps they may do lookups.
Trish