The Nintendo DSi is compatible with most SD Cards with the following specifications:
Memory Capacity: Up to 32 GB (Gigabytes)
Type: The Nintendo DSi supports standard SD cards as well as high-capacity SD cards (SDHC) over 2 GB in size. This includes miniSD and microSD when used with their respective card adapters.
Speed: SD Cards with a slow speed may experience slow transfer time when loading files, or may not work at all. Slow transfer times can also occur with SD Cards that have a great number of files on them.