My guess. What has to be factored in is that the parties back then were decided on much different issues than today, and conservatives might favor more government then where they'd favor less now, and vice-versa. However, there were a few, like Jefferson, that stand out as fundamentally liberal for their times. Adams on the other hand, might be economically progressive to a certain extent, but also socially conservative and moderate on foreign policy. It's a difficult game, no doubt. As well, by modern standards, many presidencies are mixed bags.
John Adams - Moderate North-Eastern Democrat, favorable to banks and the military, though also in favor of nationalist economic policies
Thomas Jefferson - A variety of diffferent ideologies, though definitely a left-libertarian to a large extent who also has some class issues (despite himself coming from the upper class)
James Madison - A Republican version of Jefferson--anti-taxing, anti-spending though he goes through a Dubya-like transformation on foreign policy after 9/11.
James MonroeJohn Quincy Adams - A Simfanic Democrat with culturally Republican tendencies.
Andrew Jackson - War-supporting Ron Paul
Martin Van Buren - Given Van Buren's political skills, he'd probably be a bit different than he was in the 1830's. Assuming he's a Democrat, he'd likely be economically moderate and socially liberal.
William Henry Harrison - Tossup here. War hero though, so in today's world of politics that could whipe all else aside.
John Tyler - I believe his still-living grandson is a Republican and part of his local party, so there's that. Paulesque, to be sure.
James K. Polk - Pro-war, libertarian on economics, etc.
Zachary Taylor - A nationalist and war hero, so yeah.
Millard Fillmore - I guess.
Franklin PierceJames Buchanan - Some uknown constitutionalist Democrat who peopel on the internet suspect is gay.
Abraham Lincoln - Given what I know of his domestic policy, I'd say Democrat. However, as with many, it's hard to say given his geographical location and background what he'd be today.
Andrew JohnsonUlysses S. Grant - Strong military dude, pro-gold, etc. Grant would definitely be a Bush supporter in the wake of 9/11, and supported Reconstruction of his own country's South, so why not of Iraq?
Rutherford B. Hayes - Supported "sound currency". I know little else of him, so yeah.
James A. Garfield - Of what little I know of him, I know that he supported silver as opposed to deflationary/stable gold currency.
Chester A. Arthur - Vetoed an expensive improvement bill, improved the navy, signed some anti-immigrant bills, as I recall.
Grover Cleveland - Another libertarian Republican. Likely wouldn't be politically successful at all in today's New York.
Benjamin Harrison - When unsure, I go with the default.
William McKinley - Difficult time with this one. Though his presidency as it is known screams "OMG! Imperialist Republican!", there's quite much more to the man than is communicated by the beginner's version of his presidency. Were one to take his congressional career, they'd probably say Democrat. Given, however, his presidency's foreign policy and the people who backed him for the office, I'd say a rather out of place Republican.
Theodore Roosevelt - though a very hawkish one, and quite the odd bird in his party.
William Howard Taft - I assume.