You say "Military Coup" like it's a bad thing.
The constitution of Honduras has an article 239 which specifically prohibits not only the reelection of a president, but also proposing to reform it. It's a neat idea - remember I mentioned a couple of weeks ago that Thomas Paine had recommended something along the same lines with respect to monetary policy.
President Zelaya proposed a referendum to overrule (without legal justification) this article of the constitution, and was told by the Supreme Court that he couldn't. He then had the ballots printed abroad and attempted to carry out the referendum illegally, and, after votes by both the Congress and the Supreme Court, the army was ordered to arrest him. Which they did.
Hat tip to Half Sigma, whose line is that this is no coup, but a simple exercise of law.
Assuming ½σ has the legalities straight (since Honduran constitutional law is one of those odd gaps in my knowledge) I would still say that whether this is a coup is merely a question of definition. The question matters to many people because they have an unjustified prejudice against military coups. I've been thinking sympathetically about the concept of the army removing the government for a while, so the idea that a coup might be legal strikes me not as a paradox but as a ray of sunshine - if nothing else, it allows me to post some of my thinking about the future of Britain without being a terrorist.
The advantage of a definition of coup that ignores the legality is that it allows me to describe what happened even in situations, like this one, where I don't know what the law precisely is. There has been a military coup in Honduras, which I think was probably a legal one. There, isn't that an efficient description of the situation?
The thing about constitutional legalities, as I suggested in my recent post on Iran, is that they never ultimately matter because there's no forum where they can reliably be resolved, the competent court always being in effect one player in the political game. Some of the participants may be influenced by their perception of the legal situation, but that's the only importance of law.
The court made the legal decision to have the president arrested, then the army made the political decision to obey the court rather than the president.
As I said in a comment at UR, For law to be preserved, law and government have to be two different things. If the law overrules the government, then it is not law, it is government. If the government can decide what the law is, then similarly, it is not law but government.