Sue,
If you are interested in the Reivers then the broad historical background to their arrival in Ireland is that when King James I became King of England in 1603, he was already King of Scotland and so then became the first King of both countries. For hundreds of years the Scottish Borders had been fairly lawless and travellers were routinely robbed, and cattle often stolen and herded across the border by moonlight. James was particularly keen to stamp this out because he saw it as an obstacle to commerce between the 2 countries, and being joint ruler that bothered him more than his predecessors.
At the same time he had the problem of Ireland. The Spanish Armada had recently attempted to invade England and further invasions by the Spanish or French were feared. Ireland was seen as a possible jumping off point for such an invasion and understandably, the native Irish could not be relied on to support the English or resist any invasion. So the solution was to plant trusted settlers from England, Wales & Scotland in Ireland, in large numbers, to subdue the native Irish and be on hand to deal with any invasion. King James I was a Scot and so particularly favoured his fellow countrymen. Much of Ulster, was heavily settled by Scots. During the 1600s, some 200,000 Scots settled in Ireland representing something like 15% of the entire Scottish nation. They didn’t all come as part of the Plantation. Some settled in the 1640s when General Munro's 10,000 strong Scottish army was disbanded at Carrickfergus after the 1641 uprising, and a further batch came in the 1690s due to famine in Scotland.
As far as the Reivers were concerned, King James I decided to move large numbers to Ireland around 1610 onwards. He needed settlers in Ireland and he wanted to get rid of the Reivers from the Borders, or at least stop the criminality by breaking their control of that area. So moving them to Ireland was a bit of a masterstroke which killed two birds with one stone. So if your ancestors are Reivers, they probably arrived in the first 20 years of the 1600s, as part of the Plantation of Ireland.
There are no records of individual settlers at that time. We do know the names of the big landowners (Scots & English) but not of their tenants and others who followed them.
If you visit Border towns like Selkirk, Hawick, Galashiels & Jedburgh today, you will find a strong Reiver tradition with folk & food festivals every summer. You can go for a Reiver walk by moonlight and have a 16th century banquet. (The usual tourist nonsense but good fun all the same). For example, see:
http://www.hawickreivers.com
If you want a detailed read about the Reivers, a good book is Godfrey Watson’s “The Border Reivers” published in 1974, ISBN 0 709 4478 4. Plenty of bloodthirsty, cruel tales. The Armstrongs get regular mention.
http://www.borderreivers.co.uk/Border%20Families/BORDER%20SURNAMES%20%202.htm
Armstrong is I think the second most common surname in Co. Fermanagh after Maguire. Their ancestral home in Scotland was Whithaugh Castle in Liddesdale, Roxburghshire and their chief lived nearby at Mangerton:
http://www.gatehouse-gazetteer.info/AP/whithaugh.html
One of the most famous songs in Ireland, after Danny Boy perhaps, is the Parting Glass. A lament performed here by Liam Clancy & Tommy Makem. However it started life as “Armstrong’s Goodnight” and was reportedly written by Sandy Armstrong, on the eve of his execution in Scotland in November 1600 for murdering the Warden of the Middle Marches (An important Government official in the Borders).
https://www.youtube.com/watch?v=KqcdTinjKvA