Thinking about this, and it is not using kitty litter, a long term solution for handling waste might be to compost it, as SHawk suggests. IIRC, the mixing of green and brown vegetation with manure helps, becaue you need to get the temperature of the rot up pretty high.

Mixing bacteria in with your pile helps. You can buy bacteria for composting, but I have no idea how well the bacteria meant for a compost pile with grass clippings would work with animal or human waste. Most composting guides I have read warn against using either, and especially warn against it for meat-eating animals.

Anyway, my thought was that bacteria produceded to handle human waste might be the right thing to use, and I know such things are used in municipal and marine waste treatment facilities. Something like this might be a good thing to use, not that I am about to go try it: http://www.americanbiosystems.com/products/accelobac.php. Not sure how long you can store such things for eiither and still have them work.