Can a zombie or a staggered creature perform a coup de grace? I'm wonder for both 3.5 and Pathfinder.
Because of its interaction with the action economy, the option is rarely used, but in both games a creature can take a standard action in two successive turns to perform a full round action (see here for 3.5e and here under Start/Complete Full-Round Action for Pathfinder). That is, the creature, at the end of the first turn, takes a standard action to start the full-round action, then, at the beginning of the second turn, takes a standard action to finish the full round action. In both games, however, some full-round actions remain impossible for the creature to perform, but a coup de grace shouldn't be among these.