Column 16 of the 1940 census asks if a foreign-born person was naturalized and Charles said yes.
The 1930 census says he immigrated in 1906 and was naturalized, which cannot be correct because his son Charles Jr. was born ca 1901 in New York.
In the 1920 census he said he immigrated in 1894 and in 1910 he said he arrived in 1895. Either of those dates is most likely accurate because he married Mary ca 1900 in New York.
He probably immigrated to Ellis Island. There is a Chas. MCCARTHY that arrived on 23 Aug 1895, age 23, on the ship Campania. The only problem is that manifest did not ask his place of birth.
You need to locate him in the 1900 census, possibly where his oldest child was born; Charles C. Jr. ca 1901. That county is most likely where he was naturalized.
My guess is that Charles Jr. was born 7 Nov 1901 in Manhattan and that his father was naturalized in Manhattan also. Once you know the father's dob you can search for his naturalization records at http://www.italiangen.org/databaselist.stmhttp://www.italiangen.org/databaselist.stm