Birth registration didn’t start in Ireland till 1864. Prior to that you need to rely on church records to find someone’s baptism. To do that you need to know their precise denomination and roughly where they were baptised. Not all churches have records for the 1840s and of those that do, not all are on-line. Do you know what denomination the Steele family was?
Marriage registration for non RC marriages started in April 1845. If Robert junior was born c 1843 then that suggests his parents married before that. Pre 1845 records are mostly not on-line and again you need to know where the marriage took place to track down the correct church.
I had a look for marriages 1855 – 1875 in the Ballymoney registration area for people whose father was named Robert Steel(e). I found two. I do not know that either is your family but they might be. The father was a labourer in both cases. Does that tie in with any information you have? Labourers can be tricky to trace as they tended to move around a bit to follow the available work. In the first marriage the Steele was living in Drumaheglis and in the second in Seacon. Both are near each other outside Ballymoney.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1861/09603/5482400.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1867/11494/8225537.pdf
Death registration started in 1864. I searched for a Mary Steele death 1864 to 1901 in the Ballymoney registration area. The only one of an age that might be right was this, who was a farmer's widow, not a labourer's wife:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1879/06509/4874487.pdf
The only Robert Steele death was one in 1875 aged 85. It's not available on-line free at present. You would need to pay to view it on the GRONI website. You can view the original certificates on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
In 1817, the Rev Park conducted a census of the parish of Ballymoney. There was only 1 Steel(e) family living in the parish at that time and they did have a son Robert, so that might be your family. They lived in Milltown which is on the edge of Ballymoney:
Milltown
John
Steele [Steel]
Head of Family
Milltown
Mary
Steele [Steel]
Wife
Milltown
Elizabeth
Steele [Steel]
Daughter
Milltown
Margaret
Steele [Steel]
Daughter
Milltown
Jean
Steele [Steel]
Daughter
Milltown
Sarah
Steele [Steel]
Daughter
Milltown
Robert
Steele [Steel]
Son
Milltown
Agnes
Steele [Steel]
Daughter
Milltown
Martha
Steele [Steel]
Daughter
Milltown
Eleanor
Steele [Steel]
Daughter
Milltown
John
Steele [Steel]
Son
