John Baptist (Juan Bautiste) Rogers Cooper was born 11 Sep 1791 at Alderney in the Channel Islands, the son of Anne Rogers by her first husband Thomas Cooper. His mother moved to Massachusetts, perhaps after this husband's death, and it was possibly there at Charlestown, by 1802, that she married secondly to Thomas O Larkin Sr. A son by this second marriage was Thomas O Larkin born 1802 at Charlestown, Massachusetts.
John came to California in 1823 (Source) as Captain of the ship "Rover". He engaged in many trading expeditions, but also, at the Monterey Presidio, on 24 Aug 1827 he married Maria Encarnacion Vallejo, the sister of Mariano Vallejo. He was living at Monterey in 1831 (Source) His half-brother Thomas O Larkin Jr came to California in April 1832, where a year later, he married the widow Mrs Rachel M Holmes (nee Hobson).
Primary Sources
1850 US Federal Census, Monterey, California
1850 US Federal Census, Sonoma, California
1860 US Federal Census, Monterey, California
1870 US Federal Census, Ward 8, San Francisco, California
Secondary Sources
"John B R Cooper", Wikipedia
"Thomas O Larkin", Wikipedia