I have played both the NTSC-U (US) and NTSC-J versions of Klonoa 2 on original hardware and have had no issues with memory cards. Like somebody else here already said it might be an issue with the memory card or the PS2 itself.
Here are some questions to hopefully help source the problem:
What region is the PS2?
What region is the copy of Klonoa 2?
What brand is the memory card?
Never considered it might be a weird region thing or model type problem, I'll definately check later in the morning and update you as soon as possible.