The only Philip Cox in my family from around that time is Philip E Cox (born in 1880—in Coal Mountain, Forsyth, Georgia, United States). He was the son of Marion Lemuel Cox, also born in Georgia (in 1843).
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/M8LB-9WC : 22 August 2017), Philip E Cox in household of M L Cox, Coal Mountain, Forsyth, Georgia, United States; citing enumeration district ED 79, sheet 464C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0147; FHL microfilm 1,254,147.
Now, Philip A Cox (b1818) had 6 sons, but all of them lived & died in Georgia—except possibly William A Cox b1841. The only source I have regarding him is his residence (in Forsyth County, Georgia, in 1850—when he was 9 years old).
I guess it's possible he could have moved up to New York, but I don't currently have any other info on him. Here's the source of my info on William A Cox:
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MZYG-J59 : 12 April 2016), William A Cox in household of Philip Cox, Forsyth county, Forsyth, Georgia, United States; citing family 1174, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).