An idea I had. Thought of the King first, then came up with an idea for the Queen.
King Action-Duration
For the rest of the game, after you finish playing a card, if it was the first time you played a copy of that card this turn and it's still in play, play it again.
(This stays in play.)
Queen Action-Duration
At the start of each of your turns for the rest of the game, trash a Province from the Supply.
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While this is in play, when you play a card,
+1.
(This stays in play.)
EDIT: King should probably say "another card" so it doesn't trigger itself.