Jana, this is as close as I could come for immigration. The census didn't list the date until the 1910 census so that wasn't any help. He was the only Fox on this ship. I noticed the census gave his birthday from 1815-1825 so it is hard to be sure if this is the right one.
New York, 1820-1850 Passenger and Immigration Lists
Name: Christopher Fox Arrival Date: May 31, 1836 Age: 21 Gender: M Port of Arrival: New York Port of Departure: Liverpool Place of Origin: Ireland Occupation: Baker Destination: United States of America Ship: Ship Silvanus Jenkins Microfilm Serial Number: M237 Microfilm Roll Number: 30 List Number: 413