Millionaire because MLB players are rich?
Needle for steroids?
Olive because it is sorta shaped like a baseball?
Mexico because a lot of players are Latino?
Park because you might play baseball in one?
I think it is clearly park. Baseball 2 is a tough clue with card/diamond/park on the board. I would have gone the same way you did (diamond and card), because even if it's park, the other team was discussing park for truck, so we might have gotten it for free.
(They clearly are not going that way now, so I feel more comfortable bringing it up)