How about kitty litte? Someone mentioned that. Does it have the right characteristics for, um, solid matter? Liquid seems easier to deal with, at least for males; just use a gallon jug and keep it sealed shut when not in use.

I keep a hole in my backyard for disposal of.. uh.. used dog food. I've found that if I mix it about 50/50 with dried leaves, it composts very efficiently, with little smell.