Sorry for not being more precise. There are 78 pages of 1870 census for Galva, Henry county, Illinois. It will take me a bit of time to go through everything. But here is some information.

In a biography written in 1885, John the younger (JJ) was reported as having a birthdate of 7 Sep 1850. In the same bio it stated that he came to the US with his father and siblings when he was 15 after the death of his mother. That then would have been 1865 or 1866 depending on the time of year. He applied for naturalization in 1872. In that same biography, his parents were reported as John Corkill and Margaret Kermode.

Since this bio was written during JJ's lifetime and presumably he would have provided info, I have no doubt that these facts are accurate. Given the information you have found, the September baptism looks likely.

As to the census, the 1900 census reports JJ's birthday to be September 1851, so I believe we have identified his family accurately. This was the first census to report month and year of birth. Prior was just age.

John the elder and his children never actually appear as a family unit on a US census that I can find. They should be on the 1870 census but I can't find any obvious record.

Indeed I can't ever find John the Elder with certainty...that's really what sparked this whole request. The biography of JJ indicates that his father was still living in 1885 and had remarried, living in Ford County, Illinois. There is a marriage record in 1879 for a John Corkill whose parents were Robert Corkill and Esther Colkate??

In any event, the first time JJ appears on the US census is 1870. He is reported as being 20 years old. He is living with the Lewins and working on their farm. There is another Corkill (William) also living there. He is reported as age 22.

There are multiple Corkills in Galva at this time. Unfortunately, there were no addresses just simply household numbers so it is difficult to track year to year location wise. It's necessary to look for groups of families living near each other to try and identify when multiple names.