No, there is no way to do so. The 3DS will support Miis, though.
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Unfortunately Not, you will need the Nintendo 3DS.
Yes, the DSi can connect with the Wii just like an ordinary DS can with game demo downloads, new game features, and Miis in some games.
The Nintendo DS lite does not support and cannot download Miis.
I don't think you can...
In America: A Nintendo DSi is $140; a DSi XL is $160. In Japan: A Nintendo DSi is ¥15,000; a DSi LL is ¥18,000. In the UK: A Nintendo DSi is £150. In Australia: A Nintendo DSi is $300.