Smallpox was the first disease to be eradicated, what was the second (not necessarily a human ailment)?

Rinderpest.

Smallpox is one of two infectious diseases to have been eradicated, the other being rinderpest (a disease of even-toed ungulates) in 2011.

https://en.wikipedia.org/wiki/Smallpox

Rinderpest is (or was) a viral disease that affected cattle, buffalos, gaurs, antelopes, deer, giraffes, wildebeests and warthogs. Along with fever, oral problems and diarrhea, rinderpest also had a high mortality rate. Midway through the 20th century, a campaign to globally eradicate rinderpest began and the last diagnosed case was in 2001.
https://en.wikipedia.org/wiki/Rinderpest