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: ”Change this colour, and stay away from the black (colour).” [Reported by Muslim in his Saheeh.]
As for changing (the hair colour) with other than black, then no problem, or (changing it) with henna or mixed al-Katam, ( ‘al-Katam’ is a plant that gives a dark colour, from the myrtle family) so there is no problem with this if the colour changes to other than black, or between black and red.