Fiqh-us-Sunnah Volume 001, Purification and Prayer, Fiqh 1.100.

Section : The Supplication After the Azhan.

After the azhan, one should make individual supplications, as that is the time when they will most likely be accepted. Anas reported that the Prophet, upon whom be peace, said, "A supplication made between the azhan and the iqamah is not rejected."

As to the authenticity of this report, it is related by Abu Dawud, an-Nasa'i, and at-Tirmizhi, who called it hassan sahih, and added "They asked, 'What should we say, O Messenger of Allah?' He responded, 'Ask Allah for forgiveness and well-being in this world and the Hereafter." 'Abdullah ibn 'Amr related that a man said, "O Messenger of Allah, the callers to prayer get more virtues than us." He said, "Say what they say and when they finish, ask and it shall be given." (Related by Abu Dawud with a sahih chain.)

On the same subject, reported Umm Salamah, "The Prophet, upon whom be peace, taught me to say (after) the sunset call to prayer, 'O Allah, this is the beginning of Your night and the end of Your day. I have supplicated to You, so forgive me."