I am searching for more information on a COEN or CONE family that may have been from County Mayo.

Patrick COEN, b. 1814, married Catherine WALSH abt. 1840. They had 5 children:
Thomas, b. 1841
Catherine, b. 1845
Ann, b. 1846
Maria, b. 1847
Patrick, b. 1852.
The family moved to Yorkshire, England at some point and appeared in the 1861 England Census, with the surname as CONE. Some of the children had indicated in later records that their birthplace was County Mayo.