During the early-to-middle 1800s the Federalist Party (or nationalist party) was replaced by this party.

a. Populist Party

c. Greenback Party

b. Whig Party

d. Republican Party

So, the Greenback and the Populist parties arose only in 1860s - therefore we can reject those two options because of this (this is a lot later than the question asks for).

Now, we could consider the whig party, but it existed between 1833 and 1854 and there was a gap of over 10 years between the dissapearance of the Federalist Pary and the Whig party.

So the best answer is d) Republican