Peadar Livingstone was born in 1932 and raised in Castleblayney, County Monaghan. His father was a jeweller. He entered St. Macartan's College, Monaghan in 1945. Following his secondary school education, he enter Maynooth College to study for the priesthood for the diocese. He studied Celtic languages — Gaelic and Welsh. He then completed a second degree in theology. He was ordained a priest in 1957. Fr. Livingstone continued his studies at Maynooth; however, he was recalled to the diocese in 1957 before he completed his Higher Diploma in Education. He was appointed to the teaching staff of St. Michael's College in Enniskillen, a diocesan seminary in Northern Ireland. At St. Michael's, he taught Irish, history and religious education.
Fr. Livingstone was a renowned scholar in both the Irish language and local history. In 1969, he published The Fermanagh Story, a comprehensive history of the county of Fermanagh. In 1979, his work The Monaghan Story was published. He also wrote a regular column for The Fermanagh Herald, a local newspaper, under the name "Ernesense."
In 1977, Fr. Livingstone was appointed president of St. Michael's College where he introduced some disciplinary measures, including mandatory uniforms. He was appointed a curate to the parish of Donaghmoyne in 1977. In 1987, he was assigned to the parish of Clogher in County Tyrone where he died suddenly that year.
- The Fermanagh Story: a documented history of the County Fermanagh from the earliest times to the present day - Enniskillen: Cumann Seanchais Chlochair, 1969.
- The Monaghan Story: a documented history of the County Monaghan from the earliest times to 1976, was published. Enniskillen: Clogher Historical Society.
- Clogher Record. Cloger Diocesan Historical Society. 1987. Retrieved 6 July 2017.
The sudden death of Fr Peadar Livingstone at Clogher. Co. Tyrone on 8 December 1987 brought great sorrow to all of us who had the great pleasure of knowing him personally...
- Father Peadar Livingstone: Ildánach, The Clogher Record, Vol. 10, No. 3 (1981), pp. 279–283 (article consists of 6 pages), published by the Clogher Historical Society