Alright, I read this Card Guide, and it told me I have to play against Caraway in order to get the Rinoa Card.
The catch is, HE NEVER WANTS TO PLAY!
He just walks around babbling forever about the Deling City assassination mission, and then he walks away and doesn't react to anything at all, not even regular conversation.
(SPOILER)At the end of the disc, he dies, so I obviously can't ask him afterwards.

What should I do?
And no, I didn't find anything on GameFaqs.