Word for someone born in the 19th century

Solution 1:

Would it not depend in a large part on their country of Birth?

Someone born in the US in 1810 (the 19th Century) is of the Federalist Period while someone born in England in the 1880's (still the 19th Century) is Edwardian.

The only generic moniker that comes to mind is "He (pardon the pronoun) is a real 19th Century man.

Solution 2:

Nonagenerian,noun ▸someone who is between 90 and 99 years old

Centenarian. noun ▸someone who is 100 years old or older

Supercentenarian. :a person who is 110 years old or older

Assuming one of these, your source is probably 7 to 27 years old.