Well, the only Slot1 Device that supports the big SD cards is
NinjaDS, but as you can see in the pic's, the device is rather big.
If you want a normal DS-Cart sized thing, you'll need to use a MicroSD (TransFlash) kind of device.
Currently there are AceKard and NinjaPass, AceKard is harder to use, but NinjaPass is crap. Soon there will also be MicroNinja (that's from the NinjaDS company, not the NinjaPass), which will be just like NinjaDS but now normal size and MicroSD format.
Also there will be EZ5 and SuperCard DS coming, both also using MicroSD.
Ow, and there's a DSLink out already for a while, but that requires you to flash your firmware or keep switching cards with MK4-Mini...
But if you don't want to buy seperate MicroSD carts, you might want to use a Slot2 device. However, Slot2 devices using big SD carts will be big themselfs too, so expect them to stick out of the ds lite pretty much.
As you only want DS support, I think the big blue
SuperCard will be a good choice.
Slot 2 devices require you to have a passcard in Slot1 though. (or to flash your firmware, but I don't think you want that)
-edit: ow, the flashing. Flashing is modifying your DS firmware to make it able to boot from Slot2. (and allow unsigned code to be run and so) However this will make you lose you warranty and it might go wrong, which will make your DS useless... But since the passcards, it's not needed to flash the firmware anymore...