Short answer: use 'Rallies'.
This is a question about spelling, since you already realize that the plural of Rally has an es sound at the end. Either way, Rallys or Rallies, it will be pronounced the same.
There may be formal rules, but there are no official rules. No one officiates the English language, although some people try to, in vain.
So, ultimately, you would need to use your preferred or favorite style guide (such as Chicago Manual of Style, APA, New York Times) or just make up your own rule, or go with what looks better to you. This is especially the case with something so esoteric or specialized as card names of a niche card game. I personally think Rallys looks better than Rallies, and this also follows the rule for proper names; compare Reilly and the Reillys.
However, there is the professional baseball team of 125+ years, whose name is the Philadelphia Phillies. This seems to be a case of using "common noun pluralization" (philly > phillies) being incorporated into a proper noun, the name of the team. And it also shows that there is no overriding "formal rule." Or perhaps this is the rule; I'm with you: it's hard to find a rule for this (and even if we did, we wouldn't have to agree with it).
This case seems similar to the plural of the noun lady-in-waiting, and I think the plural would be ladies-in-waiting. However, I don't know if this word is used as a proper noun. It would be, if it is used as a title: Ladies-in-waiting.
Going on the previous two examples, it seems Rallies can at least not be wrong. And since I'm a baseball fan, I might have to go with Rallies, contradicting my previous predilection ("like").
Sometimes we native speakers do avoid such quandaries by "writing around" (that is, avoiding) the issue with something like Rally Cards.