I take it that you are looking deeper than just the christening since that is shown in IGI.

Castle Garden. org is listing a Thomas Corkill arriving USA from Liverpool, 28 June 1869 age 56, on board the City of Antwerp. Also on this ship is Mary J. Corkill, spinster aged 26 and Thomas Corkill aged 21.

There is no indication of relationship but the younger ones may be the children of Esther Corkill.

Len Faragher