Or... try an industrial compact flash card. I use those as both boot and PCMCIA drives on all of my vintage ThinkPads. I'd imagine they should work just as well on a 560 as well. I've had some difficulties myself with newer memory-type CF cards, whereas industrial CF cards (meant to run as a boot drive) worked just fine. And if the OP wants to stay on the cheap side, Cisco CF cards you can find on ebay fit the bill. You can find 256MB, 512MB, 1GB and so on pretty easily and for not much coin.Try smaller CF cards. I've used similar adapters in the past and all laptops - except one - would happily take a 64 MB CF card (I think a 128 MB card also worked). The remaining laptop did work fine with an 8 MB CF card (yes, eight megabytes).
Even your smaller card already exceeds the limitations of non-extended IDE CHS addressing (which is 504 MiB).