The situation:
I played against the card queen in Balamb, and purposefully lost the MiniMog card to her. She moved to Deling City.

The problem:
Then somewhere I read that in order for her to make the new cards you must lose them to her while she's in Dollet. I went to the guy dressed in black in the Deling City shopping arcade to try for the Kiros card, played 47 games, and no Kiros card.

The question:
Is it true that I needed to lose MiniMog to her while in Dollet? If so, can I win it back from her now?

The Kiros card isn't available yet, it's not that card that you get from the MiniMog. I think the Irvine card is first, from the mayor's assistant in FH... Flo. I actually forget if it's from her or the mayor, but that's what you should be looking for right now, not Kiros.

And the MiniMog I believe you're supposed to win back from the boy in the artist's room, not her. Same with any card that you're supposed to lose to her for the sidequest.

EDIT: Didn't notice you said you lost the Minimog to her while in Balamb. Yeah, I think she needs to be in Dollet. Did you actually witness her asking for it? Or did you read in a guide to lose the MiniMog to her. If you lost it to her before she actually asked for it, then I believe you should be able to win it back.

It goes like this:

-Get her to go to Dollet by winning/losing rare cards to her (she moves when either happens, so you should keep losing and winning back a rare card until she's in Dollet).
-Choose the fourth option when you talk to her when she's in Dollet (it only appears there) and lose the card she asks for.
-NOW the new card is made. Kiros, Irvine, etc. I believe Irvine is first though. I'm not 100% but I haven't played in a long time, so go get it!
-Win it back the card you lost to her by her request from the guy in the artist shop (she won't have it). But if you lost it before she even got to Dollet then she will have it.

The problem:
Then somewhere I read that in order for her to make the new cards you must lose them to her while she's in Dollet. I went to the guy dressed in black in the Deling City shopping arcade to try for the Kiros card, played 47 games, and no Kiros card.

The question:
Is it true that I needed to lose MiniMog to her while in Dollet? If so, can I win it back from her now?

Actually if you lose it while on Dollet she will leave the area and then you'll have to make her come again on Dollet to get the new cards. So basically you should lose the cards you are supposed to lose in an area other than Dollet. Keep losing cards until she goes to Dollet. Talk to her before you challenge her to a card game and she'll say the locations of the new cards (well not the exact person though but you can check a guide for that).