Shona,
The townland that Richard McCready lived in is generally called Tirgarve. It’s in Co Armagh, not Cavan. Spelling varies a lot in Ireland as you will discover. (These names are mostly anglicised versions of ancient Irish names and are often spelled phonetically.)
Ballyharridan is more commonly known as Ballyheridan. It too is in Co. Armagh, not Cavan. There are numerous places with similar names all over Ireland. Do not be confused by them. Both your families lived in Co. Armagh.
Tirgarve is in the parish of Grange, and Ballyheridan in the parish of Lisnadill. Tradition was to marry in the bride’s church, and thereafter she’d usually attend her husband’s (assuming they came from different parishes or denominations). So you might expect Eliza and family to have used Lisnadill church.
Lisnadill Church of Ireland is Anglican. That’s Protestant but it’s important to realise there are numerous Protestant denominations eg Presbyterian, Methodist, Baptist, etc so worth being specific, to ensure you search the right records). The family are shown as Church of Ireland in both the 1901 & 1911 censuses. So both sides of the family appear to have shared the same denomination. With Tirgarve being in the parish of Grange, the McCreedy family may have attended Grange Church of Ireland. Its records start in 1780. There’s a copy in PRONI in Belfast. They are not on-line there, so a personal visit is required to view them. If going, take photo id to get your reader’s ticket. (issued at the reception. Takes 2 minutes, valid 10 years). You could look up the wills I referred to as well, as they may contain leads on the whereabouts of 20th century relatives.
You can also check to see who lives on the family farm today in case they know of any McCreadys in the area.
There was a second McCready farm in Tirgarve as I mentioned before. They are likely related to your Richard. They had a daughter married in 1899 in Grange Church of Ireland, so that makes me think it was the McCready church.
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1899/10394/5784632.pdf
I checked back to see who was on the McCready farm in Tirgarve in 1832. A William McCreedy is listed in the tithe applotment records:
https://www.irishgenealogyhub.com/armagh/tithe-applotments/grange-parish.php
Spelling there is McCreedy and Terrygarve but it’s the same place the family were living 100 years later. Farmers did not move about if they could avoid it.
In the case of the Ballyheridan McCormick family, the tithe records for 1832 show a Samuel McCormick there then:
https://www.irishgenealogyhub.com/armagh/tithe-applotments/lisnadill-parish.php
The family is not listed there in Griffiths Valuation in 1864, suggesting they had either died out or moved. So that makes it very difficult to tell you precisely where that farm was within the townland.
You ask about finding Richard & Eliza’s parents. You know that Richard’s father was William and Eliza’s Arthur from their marriage certificate. Both were farmers. Death registration started in Ireland in 1864. If either died after that you might find a death certificate but not before. Richard McCready is listed in Griffiths Valuation in 1864 as tenant of the farm so I’d assume his father died before that. Likewise there’s no sign of Arthur McCormick in Ballyheridan in 1864 so he too had probably died before that. William McCreedy might be listed in the Grange burial records (in PRONI) but Lisnadill’s records were destroyed in the 1922 fire in Dublin, during the civil war.
So you probably will struggle to find much on the McCormick family, save perhaps any gravestone information but with the McCreedys you may get baptism, marriage and burial records from Grange Church of Ireland (in PRONI), as well as gravestone information. That church has a graveyard.
According to MacLysaght’s “The Surnames of Ireland”, many of the McCormicks in Ulster “are of Scottish origin, being a branch of the clan Buchanan-MacCormick of MacLaine.” So that background, the family’s religious denomination and living in Ulster all point to them being descendants of Scots who moved to Armagh in the 1600s, probably as part of the Plantation of Ireland. McCready is less clearcut but they too might be descendants of Plantation settlers.
I have one lead for you from the newspapers. Belfast Newsletter of 26th Feb 1936 reported the death of "Mary Jane, elder daughter of the late Richard McCready, Tirgarve, Armagh on Feb 23 1936 at her residence, Tower Hill, Armagh. Interred in Grange Churchyard on Tuesday 25th Feb 1936. Australian papers please copy." Her death is listed on the GRONI website. She was 67. D/1936/9/1002/44/237 You can view the death for £2.50 (sterling).
Also the Armagh Guardian of 23.7.1926 reported a minor court case between Thomas McCready and Joseph McCready both of Tirgarve for using abusive language. Newspaper reported that David McCready owned a farm at Tirgarve and his brother Joseph lived with him together with a sister Mrs Robertson. David died in 1924 and left the farm to his sister who gave some cattle to the complainant (Thomas). An auction was arranged but Joseph McCready would not allow it to proceed and threatened with a stick anyone who tried to enter the field where the cattle were. Defendant was said to have had a creditable record with the RIC (ie he had been a police officer), had enlisted for the Boer War and served in France with the South African Forces. Case was remitted to a later court. I don’t know the outcome.
Armagh Guardian of 3rd June 1938 mentions the wedding of Miss Lily Downey, 3rd daughter of the late Mr William Downey and Mrs McCready, Tirgarve, to Edward Lewis, Scotch St Dungannon. Married in Grange Church. I’d guess from that that Mrs McCready had remarried, but you would need to dig a bit more to find out.