I think Irwin was spelt in several ways in older records. I did not search in the irish census before 1901 for the fragments that survive on the national Archives website. As one is clutching at straws, heres how my hunt used existing resources and resulted in a possible follow up. Wait until you hit a brickwall in say a months time and then go through all the sources I mention and see if you can have a sensible short list for the father possibly Thomas and then go Church record hunting if they exist.
Robert leaves in 1844 so he is not in Griffths primary valuation,a census substitute about 1862
http://www.askaboutireland.ie/griffith-valuation but his father should be if he is still alive.
So consider Thomas ‘s the possible father, as a a very young father say 16 in 1823, then he would be in 55 years old 1862 , if he was 45 in 1823, then he would be 84 yr old in 1862. About 30 years fefore Griffiths a very limited listing known as The Tithe Applotment Records exists online at
http://www.irishgenealogyhub.com/antrim/tithe-applotments/ So starting with Thomas Irwin in Griffiths, one has 5 civil parishes to search
1. Ahoghill Antrim Irwin Charles Ballyminstra Ahoghill Antrim
Irwin Francis Ahoghill,(Carmacmoin) Ahoghill Antrim
Irwin John Ballylummin Ahoghill Antrim
Irwin Mary Ballyloughan Ahoghill Antrim
Irwin Robert Straid Ahoghill Antrim date 1862
Irwin Thomas Tullaghgarley Ahoghill Antrim date 1862
Then checking The tithe Applotment Records, we have just
Irwin, Andrew Townland: Loan Year: 1825 so that’s disappointing unless Thomas father was Andrew Irwin
2. Ballinderry AntrimIrwin Thomas Ballymaclose Ballinderry Antrim in 1860s
Then checking The tithe Applotment Records, we have
Irwin, James Townland: Crewpark Year: 1833
Irwin, John Townland: Ballymaclose Year: 1833
Irwin, Richd. Townland: Legatiriff Year: 1833
Irwin, Thos. Townland: Ballymaclose Year: 1833
Irwin, Wm. Townland: Ballymaclose Year: 1833
Irwin, Wm. Townland: Legatiriff Year: 1833
And so on for
3. Ballycor AntrimGriffiths list Thomas Ballyalbanagh Ballycor
The tithe Applotment Records No records atall
4. Connor AntrimGriffiths list Thomas Tullynamullan Connor
The tithe Applotment Records No Irwins
5. Craigs AntrimGriffiths list Thomas Tullaghgarley Craigs
The tithe Applotment Records No records atall
However that is straw clutching
The existing church records from PRONI church records quide online includes as an example BALLINDERRY, CO. ANTRIM
C.I. Ballinderry (Connor diocese)
Baptisms, 1806-71; marriages, 1805-45; burials, 1823-
71; vestry minutes, 1790-1870 and 1929; extracts
from baptisms relating to the Higgins family, 1806-37. MIC583/14; T/1572
MOR. Ballinderry
Baptisms, 1754-1817; marriages, 1784-1800; register
of members, 1755-1816; ministers’ diaries, 1768,
1803-04, 1810-17 and 1842-90, which include
baptisms, marriages and deaths, and lists of
members; history of the church from 1750 and
published 2000.
MIC1F/1; CR/9
P. Ballinderry
Copy of financial report showing the amount paid by
each seatholder to stipend and to the Sustentation
fund, 1888-9.
CR/3/20
R.C. Aghagallon (Down and Connor diocese)
[Part of Ballinderry parish is in the Roman Catholic
parish of Aghagallon – see under AGHAGALLON and
part is in the Roman Catholic parish of Glenavy – see
under GLENAVY]
Good luck, hoping others will join in and give you direct leads
JimG