Abu Hurairah reports that the Prophet said: “Whoever fails to pray the two [sunnah] rak’at of the fajr until the sun rises, [he should then] pray them.” This is related by al-Baihaqi. About its chain an-Nawawi says it is good.
Qais ibn ‘Umar relates that he went to the dawn prayer and found the Prophet praying fajr. Although Qais had not prayed the sunnah prayer, he joined the Prophet sallallahu alehi wasallam and prayed with him. When he had finished salatul fajr, he prayed the two rak’at (sunnah) prayer. The Messenger of Allah passed by him and inquired: “What is this prayer?” Qais then informed him of all that had happened. The Prophet kept silent and did not say anything. This is related by Ahmad, Ibn Khuzaimah, Ibn Hibban, at-Tirmizhi, Abu Dawud, and Ibn Majah. Al-‘Iraqi says its chain is hasan.
Ahmad, al-Bukhari, and Muslim relate from ‘Imran ibn Hussain that, during a journey, the Prophet slept past the time of salatul fajr and when he woke he waited for the sun to rise a little and then he ordered the mu’zhzhin to make the azhan. Then, the Prophet prayed the fajr sunnah, after which he ordered the iqamah to be made and prayed salatul fajr. It is apparent from this hadith that one is to make up the sunnah prayer before or after the sun rises, regardless of whether only sunnah prayer is missed or both sunnah and fard are missed, and whether there is a valid excuse or not. It may be made up by itself or with the obligatory dawn prayer.