Be sure that you are saving a PlayStation 2 game to a Memory Card (8MB) (for PlayStation 2). PlayStation 2 games cannot be saved to a PlayStation Memory Card and vice versa.
Why did you buy a PSOne memory card for your Playstation 2?
I think your main problem is that reason. You need to buy a new Playstation 2 memory card.
If it is possible that one can save a PSOne game, on their Playstation 2, with a PSOne memory card, then I think that your PSOne memory card is defected. But, I strongly recommend that you should buy a Playstation 2 memory card, since you have a Playstation 2 console.
But, try to delete the game saves on that memory card, if the formatting didn't work. If, it still doesn't work, then buy a new memory card.
