I know this is an old thread, but just wanted to add... The best deodorant I've ever used is just equal parts of baking soda/corn starch with enough coconut oil mixed in to make it the thickness I like. I'm allergic (break out in a terrible itchy red rash) to normal deodorants and even the deodorant stone, and I have tried every natural/alternative deodorant out there and nothing works as well as this. I love the slightly coconutty smell of it, too.
Oh, and I have also used it between my thighs while wearing a skirt and had good results.