Was there a coup in Honduras? The case that there was not a coup is pretty strong.
The basic argument is that the attorney general, supreme court of Honduras and Congress of Honduras had the legal authority to remove, and did remove, the President, and that the use of the military to carry out this order was not contrary to the law of Honduras.
There is certainly no doubt that the deposed President was behaving badly. He was defying a court ruling regarding a unconstitutional referendum to extend his own term. He wasn't impeached by the Congress of Honduras, but there is no natural law that makes a Congress a proper arbiter of that impeachability while excluding a supreme court for making that kind of determination.
Equally important, the Congress, Supreme Court and Attorney General of Honduras remain in power, and the acting President is a civilian. Normally, one thinks of a coup as an event that displaces the entire civilian regime and installs the military in its place, at least temporarily. There is no indication that the institutions of the government of Honduras are so dysfunctional at the moment that they are incapable of adjudicating the legitimacy of the incumbent President. Likewise, the military has not presumed the power to change the constitution of Honduras outside legal channels.
The change of power was also bloodless. The deposed President was removed from office and involuntarily exiled from his country, but he was not physically harmed, imprisoned, kept ex communicado, detained in the place to which he was exiled, or had his property confiscated. His relatives have not been held hostage. No one else was seriously injured or killed as the military removed him. His four year term was close to its end in any case, and he was not eligible to be re-elected.