Was Fernando Lugo's removal a coup? Loads of people, including him, have been weighing in on this, but generally in a pretty vague way (my personal favorite is "golpeachment").
Here is the definition from The Oxford Companion to Politics of the World. The entry was written by Claude Welch, an expert on civil-military relations:
A nonconstitutional change of governmental leadership carried out with the use or threatened use of violence is known as a coup d'état.
The "nonconstitutional part" is immediately a problem. At this point, no one contests the impeachment and removal per se, but rather the time Lugo was given to defend himself. But I have yet to hear Lugo himself say the process was nonconstitutional. As for violence, none was used. The army proclaimed itself neutral, but is not an apolitical body so we don't know what was said in private. However, Lugo has made no indication of a threat of violence (though after the fact he used that as an excuse for why he accepted the situation, which makes little sense because now he's calling for resistance). As he has said, though, for him it was constitutional enough that there is no legal avenue for his reinstatement.
Or take the definition from 21st Century Political Science: A Reference Handbook, Volume 1:
If a transfer of power occurs according to some legislative action or constitutional directive, a coup has not taken place (p. 125).
My concern is that "coup" become so broad and so vague as to diminish the term entirely so that it becomes "change of government I strongly dislike," as has occurred with "terrorism," which to many people these days means "people I strongly dislike." They mean everything so ultimately they mean nothing.
As is quite common, maybe we can add some adjective to "coup" as a qualifier. That's fine as long as it conveys the legal process and the lack of violence (generally meaning lack of military action).
Now, this leaves open the problem of what constitutes legitimate impeachment. But that's for another day.