Fiqh-us-Sunnah Volume 002, Supererogatory Prayer, Fiqh 2.005A.

Section : Second rak'ah of fajr.

In the second rak'ah he would recite: "Say: O People of the Book, come to a statement that is common between us and you; that we shall not worship any save Allah and we shall not associate any partners with Him and we shall not take others as Lords besides Allah. And if they turn away then say: Bear witness that we are they who have surrendered unto Him."

He also reports, in a version recorded by Abu Dawud, that in the first rak'ah the Prophet sallallahu alehi wasallam would recite: "Say: We believe in Allah..."

In the second rak'ah he would recite: "But when Jesus became conscious of their disbelief, he cried: 'Who will be my helpers in the cause of Allah?' The disciples said: 'We will be Allah's helpers...' "

From the report of 'Aishah, mentioned earlier, it is concluded that it is permissible just to recite al-Fatihah in each rak'ah.