akuperma: A treaty can only be ratified in the Senate if it is between the U.S. and a foreign nation. Since the State in question will still be a part of the U.S. at the time it may seek secession, a treaty is not a possible avenue and is irrelevant to the issue.
A constitutional amendment is indeed the only avenue to legally secede. But passing a constitutional amendment, as you know, is very difficult as it require the acquiescence of 3/4 of all the States in addition to requiring 2/3 of both houses of Congress (or 2/3 of State conventions.)