Hi sjme
Welcome to Rootschat You say Peter snr was born in Paisley abt 1837?
Are you sure about that?
The list of children you provided
John 1860 (your grandfather),
Peter 1862,
Helen 1864,
Agnes 1864,
Jane 1866,
James 1868,
Janet 1872,
Elizabeth 1874
William 1874
Looks for all the world like they belong to the following family (with 3 more children born after dau Elizabeth, and possibility child Helen b 1864 and Janet 1872 did not survive infancy)
1871: Paisley Middle Church9 Back Sneddon Street
Head: Peter STEVENSON 33, Iron Stone Miner, b Bannockburn, Stirlingshire abt 1838
Wife: Elizabeth 31, b Paisley abt 1840
Son: John 10, b Paisely abt 1861
Son: Peter 8, b Paisley abt 1863
Dau: Agnes 6, b Paisley abt 1865
Dau: Jean 4, b Paisley abt 1867
Son: James 2, b Paisley abt 1869
1881:Dalziel, LanarkshireGlenhead Old Camp
Head: Peter STEVENSON 43?, Coal Miner, b Bannockburn Stirlingshire
Wife: Elizabeth 41, b Paisley
Son: John 20, b Paisley
Son: Peter 18, b Paisley
Dau: Agnes 16, b Paisley
Dau: Jane 14, b Paisley
Son: James 12, b Paisley
Son: William 7, b Paisley abt 1874
Dau: Elizabeth 5, b Paisley abt 1876
Dau: Catherine 3, b Dalziel abt 1878
Son: Robert 1, b Dalziel abt 1880
Son: Alexander C. 1month, b Dalziel 1881
These two Census have the father/husband as born in Bannockburn Stirlingshire
Cheers
AMBLY