Lynn,
The family were Church of Ireland (Anglican). The main parish church (in Loughgall town) has records from 1706 onwards (with some gaps). There are also churches nearby at Annaghmore and Charlemont but their records start much later.
Ballymagerny is a townland. That’s an administrative land unit which is unique to Ireland. It’s not a town and it’s not a parish. It’s in the parish of Loughgall and is 263 acres of agricultural land. In the 1901 census it had around 21 famrs and labourer’s houses with a population of 263. With the exception of 1 car driver, all the adults were engaged in farming.
http://www.census.nationalarchives.ie/pages/1901/Armagh/Loughgall/Ballymagerny/
The modern Ballymagerny Rd goes through the middle of the townland, a mile or so north of Loughgall, off the Red Lion Rd.
The Newry Telegraph of 12th May 1829 lists Joseph Jackson of Ballymagerny as applying to register the freehold of his lands. (This would have been to ensure he was a registered as a voter for elections).
The Warder & Dublin Weekly Mail of 26th Sept 1846 mentions the marriage between A J Pringle of Sallyvale, Grange and Martha, second daughter of Wm Jackson of Ballymagerny, at Loughgall church on 10th September.
I can’t find any other mention of the family in the newspapers.
You ask why the family moved away. I can’t answer that specifically but would assume it was for the same reasons that 8 million other people left Ireland in the 1800s, namely economic betterment.
Ireland has very few natural resources (no oil, coal, iron ore etc) and so did not benefit from the industrial revolution in the 1800s, the way Scotland, England, the US, Canada & Australia did, which created hundreds of thousands of comparatively well-paid new jobs in new industries (coal mining, steel making, railways, ship building etc). So that was a big pull factor. There had also been a huge population explosion in Ireland going up from about 3 million people in 1750 to 8 million in 1830. There simply weren’t jobs for all those people. In much of Ireland the only employment was subsistence farming topped up in Ulster and one or two other areas with a bit of linen weaving. And then the straw that broke the camel’s back, along came the famine, numerous times throughout the 1800s. The worst period was when the potato crop failed almost completely 3 years in a row in the late 1840s, and then partially several more years after that.
Other factors led to the continued emigration too, eg early mechanisation on farms. With new machines to turn the soil and plant seed, farmers no longer needed an army of agricultural labourers to help on the farm. So those jobs were rapidly disappearing. Likewise mechanisation had led to linen factories being set up in places like Belfast. These made home weaving uneconomic and so also upset the labourer’s family economy. Agriculture was the biggest single employer in Ireland, but it was mostly a barter economy. Few people had any ready cash save what they could make from weaving or any government sponsored work such as building new roads. So when the opportunity arose to get jobs with a regular wage packet, as opposed to a few pence from your father each week, the decision to migrate wasn’t really all that hard to make. So it was as much about economic betterment as anything.
Your family were farmers and would have been better off than most of the population(especially if eligible to vote because you had to have land over a certain value to be eligible to vote, so Joseph seems to have had had a reasonable sized farm. It’s possible to get the actual size from the tithe applotment records on the PRONI site, but they won’t show the precise location. Normally the farm went to the eldest son. The other sons were expected to fend for themselves. The daughters were to be provided for through marriage, save sometimes for the lucky one kept back to look after her parents in old age! So most people had to leave. In your case it looks as though your family must have felt there were better opportunities elsewhere. The sale of the farm would have paid their tickets and given them some capital on arrival in Canada. It looks as though most of the other Jacksons must have done something similar. There’s a likely widow there so I’d assume her husband died and her sons had already gone.
I found some other Ballymagerny Jackson marriages to give you some information on the other families. Some of these may have stayed in Ireland.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1845/09284/5361719.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1848/09340/5381998.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1846/09300/5367229.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1849/09360/5389682.pdf
Marriage registration started in Ireland in April 1845. Prior to that you have to rely on church records. Not all churches have early records and of those that do, not all are on-line (especially for Protestant churches).
I searched the PRONI site and it has a record of Thomas Jackson of Ballymagerny having probate granted on 26thMay 1781. The will itself was lost in the 1922 fire but it at least give you a name of a possible ancestor from the 1700s.
The PRONI site also details 4 Jacksons from Ballymagerny who voted: Henry in 1815, Thomas 1815, William 1817 & Joseph 1817. To have a vote they would again have had to had a specified amount of land. So they were all farmers.
You could probably learn a bit more about your family by going through the Loughgall Church of Ireland records. Some of them are on rootsireland (subscription) but you need to check what years they cover. You may find that they don’t have the earlier years (that’s quite common with that site). In which case you would need to go to PRONI in Belfast and search them there. (Or get a researcher to do it for you).
You could also search the register of Deeds records for mentions of your families. They are on-line on the LDS site and there is a copy in PRONI. Sometimes in those records in the 1700s you get 3 lives leases which provide names and ages which can be very helpful.