During Prayer, it is preferable to make du`aa’ when prostrating and after reciting the last Tashahud. It is part of the Sunnah to recite the du`aa’ using Qur’anic verses or hadiths that contain supplications. There is also nothing wrong, as far as Islam is concerned, for one to make du`aa’ for things of this world as long as one does not implore Allah to achieve something haram.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: The general rule of salah (Prayer) is that we should keep it as it is: A sublime act of communion with the Lord of the worlds; the spirit and form must be sublime; we must not introduce profane acts and words. Ordinary speech of mortals should be of limit. But while entreating or beseeching Allah’s mercy, it should be a warm and sincere outpouring of the heart. So one needs to keep to the letter of the prayers transmitted from the Prophet (peace and blessings be upon him) but one can exercise a certain liberty in using words that are in keeping with the sublime nature of salah. The Prophet (peace and blessings be upon him) is reported to have said, “Salah is such that one cannot indulge in ordinary human speech, it is intended for dhikr Allah!”
The above Prophetic imperative has been interpreted in two different ways by scholars, one group insisting that one can only use expressions of Qur’an and Hadith, while others take a more liberal view that one may use words and expressions that may not be part of Qur’an and Hadith but still come under dhikr (remembrance of) Allah.
Therefore, we find examples in the traditions to the effect that the Prophet (peace and blessings be upon him) on a number of occasions not only condoned but also applauded genuine, spontaneous expressions of glorifications and supplications from his Companions. Thus, we read in a well attested tradition that one of his Companions once burst out in his expression of praise of God saying, Rabbanaa laka al-hamdu hamdan katheeran tayyiban mubaraka feehi (Our Lord, to You alone belong all praise: abundantly, prolifically, and blessedly). Upon finishing the prayer, the Prophet (peace and blessings be upon him) asked those around him, “who had uttered those words?” and upon being told who it was, he said, “I saw angels vying with one another rushing to lift those words (to Allah)!” There are also authentic reports from a number of eminent Companions, including the Pious Caliphs, improvising supplications and prayers in their Prayers.
Based on these and other evidence, the most authentic view of scholars is that we are allowed to offer whatever prayers and supplications we wish to in our salah in our own words, so long as we keep in mind the sublime nature of Prayer. The ideal occasion to offer such free supplications and prayers is either in sujud or after the final tashahud and salawat, prior to salams. It is stated in an attested tradition that the Prophet (peace and blessings be upon him) said, “A person is closest to his Lord while he is in a state of prostration; therefore, offer prayers freely while you are in that state, for your prayers are more likely to be heard.” There are also other traditions from the Prophet (peace and blessings be upon him) to the effect that we can freely offer supplications and prayers before freeing ourselves from Prayer with salams.
In conclusion: We are allowed to offer free prayers and supplications pertaining to wellbeing and welfare of both worlds—provided we keep in mind the sublime nature of salah.