Hi Ken
As far as naming patterns go, the key - if it existed (if they adhered to pattern) would be with Harriet and James' children and you would need to be as certain as you can be that you have all the names of any children born to them - including any who may have died in infancy:
First son after James' father - James (correct).
First daughter after Harriet's mother - what was her mother's name?
Second son after Harriet's father - what was her father's name?
Do you know if there were any children born to James and Harriet who died (especially in that gap - 1856 to 1860)?
Nothing is hard and fast, but my take is that the Scottish naming pattern is so named and such a useful tool, because it was heavily and widely used. James and Harriet's children would not expect to be traditional pattern-key in this search in that, their children would then be named after James and Harriet, and after their spouse's parents. Often, Scottish families who moved away from Scotland or where they marry a non-Scot, one sees a marked change in the way children are named, perhaps not the first generation (eg: James & Harriet) but in the next (eg their children) - as if they were released from bounds of tradition' and decided on a partial mix of tradition,and also introduced their "own" preferrred names. It is also so with occupations - your James was a Stoker all his life in Lancashire; however, prior to that he may have been quite differently occupied if he was in Scotland or stayed in Scotland - ie: his English occupation may well be a result of his "change of life" from Scotland to England.
Having nothing else to go on, looking for a James ALLISON born abt 1824, poss West side of Scotland, to a father named James who was a Farmer (for farmer also consider "Ag Lab" - marriage records often 'inflated' the occupation Ag Lab to Farmer!!)
Looking on the IGI:
There is one possibility on West of Scotland which may be worth running with, if nothing else than to eliminate:
James ALLISON son of 20 Feb 1823 - Inchinnan Renfrewshire
Parents: James ALLISON and Jean REID
IGI: James ALLISON and Jean REID married 1817 Inchinnan
All Issue to same named parents - all Inchinnan
John 1818/1819
Jean 1820
James 1823
Matthew 1824
Agnes 1826
The fact this family stops here - either IGI records are incomplete (I'm not sure what coverage IGI has for Renfrew?), the family moved out of Renfrew, or one of the parents died (I would suspect the latter?)
Running with that family.......
1841: Inchinnan, Renfrewshire
Ref: Parish 566, ED 2, Folio 2, pg 6
Address: Lookinsford
James ALLISON 60 Ag Lab, b RNF (abt 1781)
John ALLISON 22, AG Lab, b RNF (abt 1819)
Jean ALLISON 20, Ag Lab. b RNF (abt 1820)
Ann ALLISON 12, b RNF (abt 1829)
Walter ALLISON 10, b RNF (abt 1831)
Cannot find IGI births for Ann and Walter - the 1841, unfortunately doesn't indicate if they are james children (from a 2nd marriage??) or perhaps other relatives.
Son James (per IGI) may be here:
1841: Inchinnan, Renfrewshire
Ref: Parish: 566, ED 3, Folio 3, pg 2
Address: Oldmains Stable Loft
James ALLISON 15, Ag Lab - b RNF
He seems to be living with 2 other young male Ag Labs in the Loft - but the previous Household, is the ALGIE farm - probably their employer (a son of the ALGIE family is John, age 15)
In 1851:
Cannot locate James Snr, Jean (may have married) or Walter.
Anne may be the IGI Anne ALLISON b abt 1828, married in Jan 1846 Inchinnan John WALLACE (he died Jan 1872) (Where is she 1851, 1861)
James Jnr (as presumed per IGI birth) looks like he is still with the ALGIE's:-
1851: Paisely Abbey, Renfrewshire
Ref: Parish 573, ED 1A, pg 5
Address: North Cardon Old
Servant: James ALLISON 26, farm labourer, b Inchinnan
On Farm of John ALGIE age 29, who was also born Inchinnan.
John may be here (interesting there are CAMPBELL's in the house)
1851: 54 Water Street, Barony Lanarkshire
Ref: Parish: 622, ED 9, pg 18
Head: Elizabeth DONALDSON 56, Seller of Milk, b Paisley RNF
Son: Archibald DONALDSON 31, Grain Lab, b Glasgow LNK
Dau: Elizabeth DONALDSON 18, Servant, b Glasgow LNK
SisterInLaw: Alex'r CAMPBELL 35, b Campbelton ARG
Grandau: Elizabeth CAMPBELL 9, b Glasgow LNK
Grandson: Alexander CAMPBELL 8, b Glasgow LNK
Grandau: Margaret CAMPEBLL 6, b Glasgow LNK
Visitor: George PATERSON 58, Engineer, b Galston AYR
Visitor: John ALLISON 29, Moulder, b Inchinnan RNF
Can't find this James ALLISON jnr in the 1861?
Could he be yours! Perhaps chasing up all these Inchinnan ones, to see where they all end up.....
Cheers
AMBLY