conservative comedy is generally, much as the name implies, ancient jokes passed down from generation to generation, and very "grassroots" (?) in nature instead of being centralized around comedians (with some notable exceptions).
when applied politically it seems to be in the form of country mouse vs city mouse jokes, poking fun at the "lack of common sense" liberals have, jokes about race, and about how liberals want to take everyones money.
that is all from my personal experience.