John Coyle

I am looking for information about an ancestor John Coyle. Family members report that he was born about 1801 in Derry. He emigrated to Brooklyn New York. The date is unclear. Family reports that he married Mary McBane/McBain in 1820. They had two children Mary and William Wallace. William shows up in 1855 New York census and it appears he was born in New York between 1828-1833. Other family members doing heritage research have been unable to find additional information as to location of family in Ireland.

I would appreciate suggestions as to how to proceed.