Some more pieces to fill in the daughter's life - though not advancing the search for RGJ's parentage:
Found this in the National Library Australia newspaper archive:
rchive-irishnewsarchive-com.rp.nla.gov.au/Olive/APA/INA.Edu/Default.aspx#panel=document
Deaths: Mrs Eliza Martha COCKBURN only dau of the late Robert Cockburn Johnston died Spa, Belgium . 23 March 1880 age 55 ( so born 1825).
The father's middle name is incorrectly cited in the newspaper report…it is RGJ & AMH's daughter - she went on to marry her 1st cousin James Stuart COCKBURN:
As noted prior, Anna Maria's sister, Caroline HARTLEY married in France 1822 to William James COCKBURN. Amongst their children was James Stuart COCKBURN b 1822.
Here's James Stuart COCKBURN in 1841, in St Charles the Martyr, Devon, with mother & brother:
1841: John Street,
Caroline COCKBURN 39, Ind, b - N
James COCKBURN 16 - N
Henry COCKBURN 14 - N
Elizabeth BLIGHT 19, F.S. - Y
Here's his cousin Eliza Martha JOHNSON in 1841, Charles The Martyr, Devon
CENSUS 1841: James Street,
Robert JOHNSON, Army, 46, b I(reland)
Ann JOHNSON 41 - N
Eliza JOHNSON 16 - N
Rawson JOHNSON 14 - N
Ann TRENNER 18, F.S. - N
Their MARRIAGE: 1846
LICENSE: 11 Nov 1846 at St Andrews, Devon
James Stuart COCKBURN age 21
Eliza Martha JOHNSTON age 21
The Marriage license:
https://www.familysearch.org/ark:/61903/3:1:3QSQ-G94Y-9HNB?cc=1833719MARRIAGE: on 24 Nov 1846 at St Andrews, Devon
James Stuart COCKBURN, full age, Bachelor, Gentleman, of Union Street,
Father: William James COCKBURN, late Leiut. of the 78th Regiment
Eliza Martha JOHNSON, full age, of Cobourg Street,
Father: Robert Gudgeon JOHNSON, Late Captain of the 68th Regiment
Witness: Thomas D………?, Anna Maria JOHNSTON.
Here's the couple in 1851:
CENSUS 1851: Nr 2 Villa Rosa, Clarendon Road, St Helier, Channel Islands
Head: James Stuart COCKBURN 26, Householder, b Avranches, France, British Subject
Wife: Eliza COCKBURN 26, b Avranches, France, British Subject
Son: James WS COCKBURN 3, b Charles, Plymouth
Daughter: C F COCKBURN 1, b St Peters, Guernsey
BIRTH/BAPTISM of the son:
https://www.familysearch.org/ark:/61903/1:1:Q2MS-TG1KBaptised 11 Oct 1847, Plymouth, Devon
James Whidbey Stuart COCKBURN
Son of James Stuart COCKBURN, Gentleman & wife Eliza Martha.
Abode: South Devon Place
BIRTH/BAPTISM of the daughter:
Baptised at St Luke Chelsea on 22 Oct 1854
Caroline Frances COCKBURN, born Dec 1849
Dau of James Stuart COCKBURN, Gentleman & wife Eliza Martha.
Abode: South Parade
DEATH/WILL 1863/64:
James Stuart COCKBURN, Storekeeper in the Anglo-Chinese Service, died 21 Aug 1863 Shanghai, China. Admin 15 Oct 1864 at the Principal Registry to Eliza Martha COCKBURN of 5 Rue Comte de'l Equerre in Bruges, Belgium, Widow the Relict of the Deceased
Cheers
AMBLY