I'm by no means a Shakespearean expert but I'll take a punt at this and start the ball rolling with two.
Henry Tudor, Earl of Richmond (later Henry VII) kills King Richard III, and
Macbeth or possibly his wife, Lady Macbeth (because it can be construed that King Duncan was still alive when Macbeth left him).
King John was also killed but by an un-named monk who might not have been a character in the play.
Claudius may have killed Prince Hamlet's father but no actual proof is offered in the play. Hamlet bases his accusation on a conversation with a ghost added with Claudius' reaction to a supposed re-enactment of the event.
The answer also depends on how a 'king' is defined.
Edward V was nominally the King of England by right of inheritance but had not been crowned and was technically still a prince when killed by James Tyrrell on Richard III's orders (according to the Bard).
Additionally, if you'll allow a 'caesar' (as some definitions do), then the answer might be two PLUS as many senators as the props department can supply with daggers.
Don't forget that Prince Hamlet kills his stepfather who was a usurping king - or maybe not usurping. The rules on inheritance of the crown weren't always what we are used to now, and the crown in some places could pass in all sorts of direction quite legitimately. An alleged murder might affect things, or might not.
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