Had there been such a thing as a confederate supreme court I wonder what they would have thought of the Davis suspension of habeas corpus. If they followed the same legal thinking of the U.S. Supreme court I would assume that they should have found Davis in violation of the constitution as well. But we'll never know.
If you or I believe that the Constitution is a document for all times and places, for war and peace, and that the powers are delegated to a specific party for a reason, then I would have to agree that it was unconstitutional for Lincoln and Davis. Amend the Constitution if you want, but do not deviate from it until then.