Yeah, the only way should be made more complicated is if you're knifed or you commit suicide.
How I'd have it setup:
When a player kills another player, the killed player drops a diamond, but doesn't loose one of his own. Any player can grab that diamond the killed player dropped, not just the killer.
If a player commits suicide, they loose a diamond.
If a player knifes a player, the knifed player looses a diamond, and the killer instantly gains the diamond.
This is about as simple as it can get. Still has some perks for strategic play but anyone can join and learn the rules in just a minute of gameplay.
And for teamplay it could simply be a team pot for all the diamonds. If any player is knifed or commits suicide, the team loosed one diamond from their collection.
Areas for consideration:
If you make someone commit suicide, or knock someone off a ledge to there death(where you are credited with the kill). It would drop one at their death point if its within playing boundaries. However if the player simply kills themselves or jumps to death, no diamond is dropped.