Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The dyeing of the eyebrows is permissible because there is no text that prohibits it. So it stays on its origin, as it is not considered to be thinning the eyebrow which is forbidden. It is also not considered as changing the creation of Allah. However, it becomes Haram for the woman to do so if someone has asked for her hand for marriage, because the person who proposes for marriage should see the woman in her natural condition.
We usually notice that the person who proposes for marriage does not carefully look at the woman the first time; therefore the real colour that a person sees when he is near the woman does not appear.
It is also not permissible to do so if there is an imitation of the Kuffar, as Allah forbids us to imitate them.
Regarding the colour of the dye, it is more appropriate to avoid black colour. It is reported in Saheeh Muslim, that when the father of Abu Bakr was brought to the Prophet (Sallallahu Alaihi wa Sallam), and all the hair of his head was grey (extremely white). The Prophet (Sallallahu Alaihi wa Sallam) thereupon said: “Change this white hair and avoid the black colour.”
Allah knows best.