This won't be the best instructable because I didn't take pictures at the beginning. But now that it's done I thought others might like to see it, and maybe do it themselves. Basically, I have a litter genie and the cartridge was empty. I went to the store to get a refill, but they didn't have any at the store I went to. So instead, I got one of the cheapo Diaper Genie refills ($5). When I got home I adapted the empty litter Genie cartridge to hold the new cheapo Diaper Genie refill.
Step 1: Cut Up the Empty Cartridge
All you need is the empty cartridge and a good knife. I used a heavy duty box cutter. All you have to do is cut away all of the plastic except for the outside part, which is what actually supports the cartridge in the litter Genie, and the four flaps as shown in the pictures. The four flaps support the Diaper Genie refill. You want to make sure to cut away all of the plastic on the bottom of the litter cartridge in the corners because if you don't the refill will be too tall and the litter Genie won't close correctly. The refill needs to be able to sink down a little. I left too much on the bottom the first time and when I went to put it in the litter genie the lids would not close all the way. **Caution!** Be very careful when cutting the plastic. I nearly cut my fingers several times because in this type of plastic, the knife moves very slow and then super crazy quick. So be careful!
Step 2: Load the Genie
That's really all I've got for this instructable. Once you have the empty cartridge cut down, just drop it in like you normally would and then drop the refill in on top of it using the flaps to support it. Then just like normal, pull out the first bits of plastic bag, tie a knot in the bottom, and shove it into the bottom of the litter genie just like normal. Close it all up and you're ready to go!