Dead skin can be one of the causes for dark underarms hence exfoliate your armpits regularly with a loofah or a natural scrub.
Use loofah sponge while in shower in circular motions to gently exfoliate the skin and remove any dead or dark skin under your arms.
Make a natural scrub using brown sugar and almond oil, exfoliate and rinse off after 5 mins.
Apply rose water or cucumber toner under your arms to remove any residues of deodorants and treat dark discolored skin.
Apply a mosituriser before using a deodorant. Use a good moisturizer right after exfoliating the armpits as well as before going to bed to keep the area soft and smooth.