Having come across this newspaper report from The Freemans Journal, 20 January 1923, several years ago and set it to one side, finally it required a deeper dive.
This newspaper article reported on the “Executions of Women by Burning”, it stated that the last recorded case of a woman being legally burned to death in Ireland took place in Limerick on 23 April 1768. In that day, Alice Moran met her fate for poisoning Joan Sullivan.

The story referenced five years later in the Cork Examiner, 28 April 1928, with Chevalier Grattan Flood, Mus. D., K.S.G, detailing other records of women being burned at the stake in Ireland.
He stated that
The fifth example to be quoted is that of Alice Moran, who was burned at Limerick, in 1768. This unfortunate woman was condemned for poisoning another woman. The bare, but pithy entry regarding her fate is thus given: “On Saturday, 23 April, 1768, Alice Moran was burned at Limerick for the poisoning of Joan Sullivan”.
Alice Moran, as far as I can learn, was the last instance of a woman being judicially burned to death in Ireland.
Cork Examiner, 28 April 1928
The Dublin Gazette of 9 Feb 1768 tells how she carried out her crime.
Although Grattan gave vague sources for his first four examples, he failed to mention where he located the report on Alice Moran’s death.
After some digging, records mentioning Alice Moran were located. The first was in the Dublin Gazette, dated 9 February 1768.

The text reads
Country-News
Limerick, February 4. Saturday last was committed to the County Goal [sic], Alice Moran, charged with going to one Buckley’s House at Brury, in this County, and giving his wife a paper, which, she said, contained some sugar, of which she desired said Buckley’s wife to eat, which she accordingly did, and in about two hours after expired in the greatest agony.
This news report gives us a location of the crime, Bruree. This is a small village in county Limerick, approximately thirty-five kilometres south of Limerick City. Today, this village is known as the home of Eamon de Valera, former President of Ireland.
The news report gives a different surname of the victim than in the 1923 report, but it was not uncommon there to be errors in names in these early records.
Notice of the execution of Alice Moran
Next, there was a notice in the Dublin Gazette, 28 April 1768

It simply states:
Limerick, April 25. Saturday last Alice Moran was executed at Gallows-green, pursuant to her sentence, for poisoning Joan Sullivan.
Although it states Alice Moran was executed, it does not state by which means the execution was carried out. It does tell us that the execution took place at Gallows Green. Gallows Green as implied by the name, was the usual spot for hangings. It was located just outside the walls of Limerick city, in the Garryowen area.
One of the most famous executions that took place at Gallows Green was that of John Scanlan on 16 March 1820. He was one of the two men who murdered teenager Eileen Hanly, also known as the Coleen Bawn.
Finally, while checking newspapers from outside Ireland, this article was discovered in Oxford Journal, 23 April 1768.

This last article states:
At Limerick Assize, Alice Moran was convicted of the murder of Joan Sullivan, by poison, and sentenced to be burned on Saturday the 23rd instant.
Now, this article was published the same day the sentence was due to be carried out, and so is not proof that the brutal sentence was enforced, but does show that it was indeed issued.
As for Alice Moran and Joan Sullivan, like so many women of their time in Ireland, there is very little information about their lives before the events of 1768.