He was born in Ashton-under-Lyne, Lancashire, the younger son of Abel Buckley and Mary Keehan of Alderdale Lodge. He was educated at Mill Hill School and Owen's College. In 1875 he married Hannah Summers (who died in 1897) and they had one son, also Abel, born in 1876.
The Buckley family owned two cotton mills in Ashton: Ryecroft and Oxford Road, and Abel became involved in the business. At his death he was described as "one of the old cotton lords of Lancashire". In 1885 Buckley inherited Ryecroft Hall, Audenshaw, from his uncle, James Smith Buckley, and was to live there for the rest of his life. He subsequently inherited Galtee Castle, near Mitchelstown, County Cork. The estate had been purchased by his uncle, Nathaniel Buckley, MP for Stalybridge in 1873.
Apart from his interests in the cotton industry, Buckley was a director and chairman of the Manchester and Liverpool District Banking Company and a justice of the peace. He was a collector of fine art, and a racehorse breeder. He died at Ryecroft Hall on 23 December 1908, aged 73.
- Obituary: Mr Abel Buckley, The Times, December 24, 1908, p.9
- Walford's County Families of the United Kingdom, or royal Manual of the titled and Untitled Aristocracy of England, Wales, Scotland and Ireland (London: Chatto & Windus, 1899)
- 'Biographies of candidates', The Times, November 26, 1885, p.3
- "Ryecroft Hall". Audenshaw Local History Society. Archived from the original on 5 September 2008. Retrieved 2008-09-04.
- "Ryecroft Hall Park". Tameside Metropolitan Borough Council. Archived from the original on 28 August 2008. Retrieved 2008-09-04.
- "Among the Galtees, Galtee Castle, County Cork by John William North: Lot Notes". Christie's. Retrieved 2008-09-04.
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1885 – 1886
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