Q Who is the last known non-natural US citizen who would have been eligible for the Presidency?
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
To approach this problem: The constitution came into effect on June 21, 1788.
This means that any person made resident before the adoption of the constitution on that date and then dying last meets this criteria. If we read this question as "who could have made a theoretical bid as candidate in a presidential election the latest under these criteria?"
Therefore I will opt for John Smith born 1787 in Yorkshire, England, immigrated shortly after birth with parents to US, made resident immediately, died 1901 at the age of 114. Disregarding appearances and fitness at that age he would have qualified as candidate in the 1900 elections. Probably beating McKinley due to Smith's much greater experience…
Did John Smith even exist? This is of course an example. It just illustrates that this question is overly broad and that it also fails on relying on robust records to search for. We need records of residentship/citizenship before 1788. But:
What time periods do they cover?
Naturalization records began in 1790 and go up to the present. However, they are much more detailed after 1906. They are found throughout the United States.
The timeframe is too big, the records too incomplete. There likely is no definite answer to this.
As the question might be read in multiple ways, and in case I missed a probably obvious to others angle:
William Henry Harrison Sr. (February 9, 1773 – April 4, 1841) was a son of Founding Father Benjamin Harrison V and the paternal grandfather of Benjamin Harrison, the 23rd President of the United States (1889–1893). He was the last president born as a British royal subject in the original Thirteen Colonies before the American Revolution (1775-1783).
This amplifies one other thing about this question: what does "eligible" really mean? The founding fathers were all traitors to the British Crown, but born on American soil, making the question of citizenship this: the first presidents were all not born as American citizens, obviously.
Seeing that not even one of the real candidates for the presidency in the history of presidential elections was not born on American soil, it seems that the original phrase was already a theoretical construct when it was written down, as obviously no-one was truly ever considered really "eligible" in pratical terms if not proven to be born on American soil.