James Downie was Master, not Captain, of HMS Coromandel. He was almost certainly the son of the Reverend John Downie, Minister of Stornoway, Isle of Lewis from 1772-1778 and his wife Charlotte McKenzie. His brother George was a Captain in the Royal Navy and was killed at the Battle of Plattsburg on 11 September 1814.
James became a Master in the Royal Navy on 22 April 1797, according to the Navy List. I am not certain of his date of birth as his birth does not appear to have been registered. He died on 8 August 1833 in Jersey, Channel Islands and his will does not mention a daughter. He was living with his sister Beatrix to whom he left a number of bequests. The other beneficiaries were his brother in law Reverend Neil Kennedy, Minister of Logie Easter, Ross and Cromarty, widower of his sister Anne who had died on 17 June 1832, and his nephew George Kennedy, then living in Jersey.
If it seems unlikely that a person with strong religious connections should father a child and abandon her, the strange case of James's brother Murdo may throw some light on this. Murdo was tried at Inverness in 1800 for murder of a child born to Ann Grant, who was almost certainly his wife Mary's sister - I have not been able to find out if Mary, whom he had married in 1795, was alive at that time. The child had been placed on the doorstep in a snowstorm and died of exposure ten days later. Murdo was found not guilty of murder but was sentenced to nine months imprisonment for exposure of a new born infant. He had married Ann Grant in London before the trial.