Fortunately once you have made it to disk 4 you can simply challenge the queen of cards and she will play each of the rare cards. The only catch is that she is (in my opinion) the hardest card player to beat due to the fact that she combines plus, random and other rules with boss, player, and GF cards. However it is still much quicker to acquire the Chubby Chocobo, Phoenix, Doomtrain, Kiros and Irvine cards this way.
To find the queen of cards on disk 4 go to the bottom of the Esthar continent and look for an area called the "Abadan Plains". You cannot see it from the world map but there is actually the crashed lunar escape pod from disk 3 on the tip of the Eastern Peninsular. Run around near the tip and eventually you will bump into it. Here you will find the queen of cards standing next to the crashed lunar escape pod.
As previously mentioned she can be tough to beat, to stand a chance of winning you are going to have to have a basic understanding of how the plus rule works. If your not sure how it works not to worry, it's pretty simple. Basically if a card is placed next to 2 other cards and both sides that are touching add up to the same number plus will occur. For example if you had a card that had the number 6 that was touching another card that had the number 4 and another side of your card had the number 7 that was touching a card with a 3 both sides add up to 10 and hence plus would occur. The game has a pretty decent card tutorial with pictures so make sure you check that out if you don't understand. Elemental does not effect plus by the way.
I highly recommend you save before each card battle as the plus and random rules may cause you to lose your rare cards to her which you definitely do not want. Also make sure you save after you win a rare card from her.
Thanks for reading, good luck!