Not a Secret Homemade Deodorant - recipe from Crunchy Betty. No Baking Soda - recipe includes coconut oil, shea butter, clay, beeswax, and essential oils. You might also try substituting cornstarch for the clay.
homemade deodorant: cup baking soda, cup arrowroot powder, 4 tablespoons coconut oil, 10 drops/shakes grapefruit essential oil (or other sent that smells good with coconut oil.) Mix dry ingredients then mix in oils.