Irish birth, marriages and deaths were not required to be registered until the mid 1840's. The earliest census were in the 1820's every ten years on. Sometimes if you know what location they came from, particularly parish, the church may have records earlier but not always.
Having said that, you may be able to find out more about where he came from things written about him where he lived, people he associated with or may have come over with or sometimes things that his children wrote down. Sometimes his death or marriage records might give where he came from or parents names, etc.
The surname Scott as known in Armagh is definately a Scott name, if he was known to be a presbyterian sometimes known as Church of Scotland, he most definately goes back to Scotland as a planter, brought over by the english to protestanize the Irish. Remember that the distance between Ireland and Scotland at Torr Head to Mull of Kintyre is only 13 miles, in fact many would finish the harvest in Ireland and then go across and help out with the harvest in Scotland. And there are stories of planters rowing across to attend church.
And now begins a wonderful journey, reading all that you can on the Scots-Irish in the hopes that your family might be mentioned. There us a great deal of information on the Scots Irish including land that may have been taken from the Irish and given to the Scot planters by Oliver Cromwell in the 1600's.
I should share with you that there are also a great number of Scott families that are also english now.
Good luck.