Ages ago I wrote that I use bicarbonate soda/baking soda and water mixed as a paste as a deodorant.
Effective as it was, you had to make a new batch everyday because it dried and mixing it everyday was a too much hassle so instead I looked for something that I could mix and it would last longer.
So I decided to mix the bicarbonate soda/baking soda with coconut oil. I think you can use any of your favourite oils, coconut oil is good because it makes a nice paste. Also I add a few drops of peppermint essential oils which adds a nice scent and freshness when applied to the underarm.
Very effective and it lasts!!!