He was born in Paisley, the third son of James Coats and Catherine Mitchell, and is deeply associated with that town. He attended Paisley Grammar School and then the University of Glasgow, at first intending to study for as a minister. However he decided to follow his father as a thread manufacturer (largely in partnership with his younger brother Thomas Coats).
He died in the Mustapha Superieur quarter of Algiers on 9 March 1890 aged 81. His body was returned to Paisley for burial in Woodside Cemetery, west of the town centre. The bronze central tablet has been stolen from the grave but the inscription is visible in silhouette. The grave is paired with that of Sir Thomas Coats, flanking the statue to James Fillans.
In the same vein as Carnegie, Coats believed that gain in personal wealth had to be balanced against good deeds in a public way. In 1870 Coats gifted his home town of Paisley a Free Library and Museum, the Paisley Museum and Art Galleries, built wholly at his expense, and intended for the improvement and education of all.
- Mosley, Charles, ed. (2003). Burke's Peerage, Baronetage & Knighthood (107 ed.). Burke's Peerage & Gentry. pp. 834–835. ISBN 0-9711966-2-1.
- "Woodside House". ntlworld.com. Archived from the original on 20 March 2014. Retrieved 20 October 2015.
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- "SIR PETER COATS". maybole.org. Retrieved 20 October 2015.
- "Former Fellows of The Royal Society of Edinburgh 1783 – 2002" (PDF). The Royal Society of Edinburgh. Retrieved 9 February 2016.
- "Paisley Museum and Art Galleries, Renfrewshire Council Collections". Art UK. Retrieved 20 October 2015.
- Paisley’s Public Sculptures: Leaflet published by Renfrewshire Council, 2008