Just a few ideas that came to mind - no idea how well they would work out, especially for monsters.
One, for each encounter each character rolls a die (GM decide dice size). If the roll is less than or equal to the character's initiative modifier they get a second card for that encounter. May want to add some negative modifier to die roll if you wish for characters with negative initiative modifiers the chance to get bonus card.
Two, each character subtracts their initiative modifier from some number, say 8. The result is an interval. The best way to describe is with an example. Say the number the DM decides is 8, character A has a initiative bonus of +3, 8 - 3 is 5. Every 5th combat of a session character A gets a bonus card. Character B with -1, 8 - (-1) is 9. Every 9th combat of a session that character gets a bonus card.
Three, each character subtracts their initiative modifier from some number, say 5. The result is the round number of each combat the character gets a second one card. Ex: Character A again with +3, 5 - 3 is 2, Starting in the 2nd round character A gets a bonus card. Character B with -1, 5 - (-1) is 6, starting in the 6th round character B gets a bonus card. If the character B is the combatant with the worst init bonus, you could just remove everyone's bonus card.
Four, mixture of #2 & #3. Each character subtracts their initiative modifier from some number, say 5. The result is an interval. Every nth round the character gets a bonus one card but the next (unless his result is a 1). Example same characters as above. Character A gets bonus card every 2 (5 - 3) rounds. Character B gets bonus card every 6 (5 - (-1)) rounds.
Just some food for thought.