if the flashcard only supports up to 2GB that usually means it doesn't support SDHC cards, except for a few rare 4gb ones, every card above 4gb is SDHC which older hardware like these flashcarts are not compatible with
making the partition 2gb or 1gb or bigger doesn't matter, because its the way the card communicates with the reader it's the problem. (SD versus SDHC)
i am not sure if the card supports SDHC, but if you don't see anyone confirming that it does support SDHC or cards bigger than 4gb, your best bet is to look for 2gb or less cards that follow the original SD specification.
If you are having problem finding MINI SD cards, you probably want an adapter to use a micro sd card, which works just fine.