It is not permissible for a woman or other than her to colour their hair with black dye, because of the statement of the Messenger sallAllaahu ‘alayhi wa sallam:
غيروا هذا الشيب، واجتنبوا السواد
”Change this colour, and stay away from the black (colour).” 
As for changing (the hair colour) with other than black, then no problem, or (changing it) with henna or mixed al-Katam,  so there is no problem with this if the colour changes to other than black, or between black and red.
 Reported by Muslim is his Saheeh.
 Translators Note: الكتم ‘al-Katam’ is a plant that gives a dark colour, from the myrtle family.