There is already a conservative third party: The Constitution Party. According to their website, they are on the ballot in 18 states, and are at various stages of approval for more. They have a presidential ticket: Darrell Castle and Scott Bradley. I’m not familiar with either of these gentlemen, but they might be better than the offerings of the major parties.
I have heard the party, which used to be called the Taxpayers’ Party, described as Christian Dominionist, but that could hardly be the case, since Mr. Bradley appears to be a Mormon. It seems to be paleoconservative, distrusting foreign wars and big corporations and holding to a protectionist use of tariffs. It is strongly pro-life, with no exceptions.