The 1851 census has him born in Lancs Liverpool, as does the 1861 census (James B Killey aged 57, merchant).
The IGI has: JAMES BROWN KELLEY Birth: 19 MAR 1804, Christening: 27 APR 1804 St Nicholas, Liverpool, Lancashire, England, Father: JOHN KELLEY, Mother: MARGARET BROWN.

Their marriage cert in 1843 should give his father's name and occupation.
Marriages Jun [quarter] 1843
Surname First name(s) District Vol Page
KILLEY James Brown Lancaster 21 297
Strickland Charlotte Lancaster 21 297

Deaths Dec 1872
Surname First name(s) Age District Vol Page
KILLEY James Brown 68 W.Derby 8b 215
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