Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.018A.

It is legitimate to recite the qunut aloud in any of the five daily prayers at those times when Muslims are faced with calamities. Ibn ‘Abbas relates that the Messenger of Allah sallallahu alehi wasallam made qunut consecutively for one month in the zuhr, ‘asr, maghrib, ‘isha, and fajr prayers. At the end of every prayer, after saying: “Allah hears him who praises Him” in the last rak’ah, he would supplicate against Re’l, Zhakwan, and ‘Usiyyah’ of Banu Sulaim, and the people behind him would say ‘Ameen’. This is related by Ahmad and by Abu Dawud adding that these three had killed the emissaries that the Prophet sallallahu alehi wasallam had sent to them. ‘Ikrimah says: “That was the begining of the qunut.”

Abu Hurairah reports that whenever the Prophet sallallahu alehi wasallam wanted to supplicate against or for someone, he would make qunut after going into ruku’. Sometimes, he would say: “Allah hears him who praises Him. Our Lord, to you is the praise. O Allah! Save al-Walid ibn al-Walid and Salamah ibn Hisham and ‘Iyash ibn Abi Rabi’ah and the oppressed [and weak] believers. O Allah, put hardship and pressure on the tribe of Muzhar and give them years of famine like those during the time of Yusuf.” He would say this aloud in some of the prayers. Also in the dawn prayer, he would say: “Oh Allah, curse so and so,” cursing two tribes of Arabs until Allah revealed: “It is no concern at all of thee [Muhammad] whether He relent toward them or punish them, for they are evildoers.” This is related by Ahmad and al-Bukhari.