I believe your Charles Burke is in the 1860 census for Brooklyn Ward 9 District 1, Kings, New York and his date of birth is listed as about 1833. He is listed as living with a Jane A. Burke age 21 born in NY - apparently his wife at the time - and Mary Duffy age 17 born in Ireland, a servant. Charles is listed as a bookkeeper in that census.
There is a naturalization record also that you might want to check into:
Birth Place: Sweden
Court District: New York
Date of Action: 23 Oct 1860