They had at least four sons, recited in the matriculation of arms to their son James George:

1. Major George Morison, d.unm and sp.
2. Henry Morison
3. James George Morison
4. John Morison

Family Search gives them these probable children:

father: James Morison
spouse: Mary S. Brown
child: Jean Main Morison
Born 15 Jul 1801, Glasgow, Lanarks

father: James Morison
spouse: Mary Brown
child: Jean Morison
Born: 19 Jul 1802, Glasgow, Lanarks

father: James Morison
spouse: Mary Brown
child: Henrietta Morison
Born: 19 Jul 1802, Glasgow, Lanarks

father: James Morison
spouse: Mary Brown
child: Henrietta Morison
Born: 30 May 1806, Glasgow, Lanarks

father: James Morison
spouse: Mary Brown
child: Margaret Wilhelmine Morison
Born: 11 Jan 1811, Glasgow, Lanarks

father: James Morison
spouse: Mary Shewan Brown
child: James George Morison
Born: 19 Aug 1813, Barony, Lanarks

All the above baptisms are to be found on the Scotlands People index.

But the other three sons reported by William Trotter are not on Scotlands People or Family Search.

May 2017, TFPL: the resolution about the sons is to be found in the Matriculation of arms to their only son James George Morison.  In this Lyon said:

(a) James George Morison was the only son of James Morison and Mary Shewan Brown
(b) James Morison the elder was the third son of James Morison of Dunbrae in the parish of Logie in the County of Fife.
(c) The brothers of James the Elder were first Major George Morison, second Henry Morison and fourth John Morison, all of whom died unmarried.

So the above son and five daughters were indeed the family of James and Mary Shewan Morison.
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He died before his son matriculated his arms in 1857.  He was alive around 1813, when his son and last child James George was born.  Between 1813 and 1855 the OPR death records on Scotlands People give 39 deaths of sundry James Morisons, though only four were in Glasgow.  I therefore have no idea when he died.
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Their marriage from FamilySearch:

groom's name:           James Morison
bride's name:           Mary Shewen Broun
marriage date:          14 Jul 1800
marriage place:         Glasgow,Lanark,Scotland
bride's father's name:  John Broun

indexing project (batch) number:  M11974-3
system origin:                    Scotland-ODM
source film number:               1042935, 1042937, 1042937
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