I was able to find Charles in all the census from 1870 forward. In 1900 it says that he immigrated in 1848 and in the 1920 Census he immigrated in 1842, but he was Naturalized in 1876. He also states his immigration info in the 1910 Census, but it was unreadable.

His son Edwin was born July 1879, with the 1880 Census saying he was born in Indiana and the 1900 Census listing his place of birth as Illinois. If he was Naturalized in 1876, I'd try either Illinois or Indiana as the state where it occurred.

I also found that Charles applied for a Civil War Pension, which he filed from the state of Indiana. Pension files are a great source of genealogical information and might be worth a try if marriage and death records didn't show his parents names. The National Archives in Washington, DC holds all Pension and Military Records from the Civil War.