Hi Roshane
1. Do contact Cavan Genealogy they can do a family search for you.
Cavan Genealogy,
1st floor,
Johnston Central Library,
Farnham Street,
Cavan Town,
County Cavan.
Tel: +353 (0)49 4361094
Fax: +353 (0)49 433149 email cavangenealogy@eircom.net
They have access to parish records which predate the civil registrations or you can search Rootsireland.ie.
2. Civil registration records are available from the General Register Office (GRO). These start from 1864. You can access the website here:http://www.groireland.ie/research.htm You would hope that if he died he died within Civil Registration
3. You can look up familysearch.org (free site)
4. I searched http://www.askaboutireland.ie/griffith-valuation/index but found nothing, but I just put in Milligan & Drung as the parish, you can put different spellings in & may get something, free site, but if father was a publian he may not have owned land
5 I searched http://titheapplotmentbooks.nationalarchives.ie and found a Peter Milligan in Kildrumsheridan, which is close to Drung, also free site
6. http://www.failteromhat.com/pigot/0096.pdf, this directory lists those who are merchants, I looked up Cootehill & did not find him, but look at Cavan and a few other places nearby in Co Cavan & Monaghan and he may turn up.
7. He did not turn up in http://www.failteromhat.com/slater/0172.pdf either.
8. I cant find any Milligans in the 1901 census, but I found 1 in 1911 aged 7 see this link, in the Cootehill Area http://www.census.nationalarchives.ie/pages/1911/Cavan/Cootehill_Rural/…
What religion did they belong to?, you might have a good chance of contacting the local church.
When you are searching, broaden it out to look for brothers using names that he called his own childen after, hopefully you might find a person to take you within the realms of Civil Registration & it would give you a good lead.
Hopefully I have given you some leads that you have not tried before, it is not a common name, which is good.
Do let me know how you got on & if I can help you further please let me know.
Regards Carmel O'Callaghan