Ashes work if you run out of lime.
I much prefer composting toilets as ashes and lime in pit outhouses keep the smell down, but don’t help compost the excrement. Sawdust from non-kiln dried lumber, chipper shredded stuff, leaf mould, dirt, etc all work well. The crap composts within a few months or less and the entire sysmtem is normally without any odor at all. All you need are a number of five gallon buckets and the composting materials, and a place to dump the buckets to compost completely. When we did it we had about 8 buckets and they partially composted in them before being dumped. It was quite non-offensive, relatively speaking, and much less offensive that a regular pit outhouse.
Link to Humanure online:
Instructions:
http://humanurehandbook.com/instructions.html
Particularly coal ashes, which my grandfather used in his outhouse. Even when he had indoor plumbing in the corncrib/vacation house, he continued to use his outhouse. He heated with coal in a huge fireplace, so there was an abundance of coal ashe for the johnny house.