I’ve been working on my husband’s Smith ancestors and recently I took a close look at the evidence I’ve found for James Ayer Smith’s birth date and place. Here’s a quick summary of where I’m at:
A compiled genealogy suggests James Ayer Smith was born 12 January 1808 in Waterville, New York.  An obituary suggests he was born 24 June 1807 in Paris, Oneida County, New York.  This is a case of unknown informants providing indeterminable information–direct conflicting evidence for the question of when and where James was born.
So, which information is more likely to be accurate?
The informant for the 1808 date is unknown, but the detailed information on the ancestors of Mary Susan Farnsworth suggests it might have been her or her daughter, James’ granddaughter, Edna Valentine Smith. This date is probably incorrect. James purchased property on 26 December 1828.  If he were born 12 January 1808, he would have been twenty years old on that day–not yet of legal age.
The1807 date in the obituary was probably provided by a family member, perhaps James’ wife Marcia or one of his three surviving sons. All four of these individuals were in contact with James, working with and/or living with him for decades. If he celebrated his birthday, they would likely known the month and day. It would be easier to misremember a year, but census records suggest a consistent pattern.
The 1850, 1860, and 1870 censuses record James’ ages as 43, 53, and 63 respectively.  If James ages were recorded as of the June 1 census date in all three years, then that would suggest he was born in 1806.
A more likely scenario is that his birth was recorded as of the day the census was taken in 1850 (August 19) and 1870 (July 15) and rounded up in 1860 when the enumerator visited twelve days before his birthday (June 12).
In 1933, James’ granddaughter, a librarian and genealogist who spent time living in James household when she was a child, agreed that he was born in 1807. 
In summary, the bulk of the family-provided information (obituary, census, and a family history) agrees that James was born in 1807 and this is supported information from a legal document that suggests James turned twenty-one before 26 December 1828. Only one record, an unsourced compiled genealogy suggests an 1808 birth year. Given that 12 January 1808 is six months after 24 June 1807, it’s possible the former is a baptismal date. Church records in the area of James’ birth should be searched.
But where was James born?
American Ancestry entry for James says “Waterville.” 
Chicago Tribune obituary for James says “in Paris, Oneida County, New York.” 
Waterville is six miles from Paris; it was likely given as a general location and not a specific place of birth.
James father is said to have settled “in the vicinity of the village [Paris], but not in it”  It’s likely James was born at home, which would have been near Paris, Oneida County, New York.
Given the consistency of the census, obituary, and family history and the weight of the deed, it’s likely James was born in 1807, possibly on 24 June, in Paris, Oneida County, New York.
1. American Ancestry (Albany, N.Y.: Joel Munsell’s Sons, 1894), 9:132; Internet Archive (https://archive.org/details/americanancestry009hugh).
2. “Obituary: James A. Smith,” The Chicago Tribune, 23 July 1875, p. 4., cols. 6-7; Newspapers (https://www.newspapers.com/image/349740584/).
3. “Deed records, 1806-1877; index, 1791-1801, 1806-1962,” FamilySearch (https://www.familysearch.org/search/catalog/235400) > Deed records v. 11-12 1828-1830 > microfilm 573087 > image 196 of 565, Collier and Merill to James A. Smith, 26 December 1828).
4. 1850 U. S. census, Cook County, Illinois, population schedule, Chicago, First Ward, n.p., dwelling 275, family 293, J A Smith; digital image, FamilySearch (https://www.familysearch.org : accessed 7 May 2018), citing NARA microfilm publication M432, roll 102. And, 1860 U. S. census, Cook County, Illinois, population schedule, Chicago, First Ward, p. 36 (penned), dwelling [illegible], family [illegible], Jas A. Smith; digital image, FamilySearch (https://www.familysearch.org : accessed 7 May 2018), citing NARA microfilm publication M653, roll 164. And, 1870 U. S. census, Cook County, Illinois, population schedule, Chicago, 4th Ward, Chicago Post Office, p. 223 (penned), dwelling 1481, family 1632, James A. Smith household; digital image, FamilySearch.org (https://www.familysearch.org/ark:/61903/3:1:S3HT-XCMC-9G9?i=223&cc=1438024); citing NARA microfilm publication M593, Roll 200; United States Census, 1870 > Illinois > Cook > Chicago, ward 04 > image 224 of 309.
5. Louise Grant Smith [SURNAME REMOVED], Memories, self-published family history, c. 1933; original created for Owen [SURNAME REMOVED] in possession of author.
6. American Ancestry (Albany, N.Y.: Joel Munsell’s Sons, 1894), 9:132
7. “Obituary: James A. Smith,” The Chicago Tribune, 23 July 1875, p. 4., cols. 6-7.
8. Daniel E. Wager, Our County and It’s People: A Descriptive History of Oneida County, New York (n.p.: Boston History Company, 1896).