In rukoo', you can say the following:





Listen to the audio of the du'a here
In Sujood, you can say the following:

Listen to the audio of the du'a here
Regarding supplicating using verses from Qur'an, there is no objection for this provided one should not intend the recitation of the Quran, rather he should intend supplicating Allaah.
Rukoo' and sujud is for supplicating to Allaah and praising him.
All the Jurists (may Allaah have mercy upon them) have agreed that the recitation of the Quran whilst bowing or prostrating is dislikable.
This is because of the narration of Ibn Abbass (radiallahu anhu) from the Messenger (salallahu alayhi' wassalam).
Ibn 'Abbas reported: The Messenger of Allah (may peace be upon him)
drew aside the curtain (of his apartment) and (he saw) people in rows
(saying prayer) behind Aba Bakr. And he said: Nothing remains of the
glad tidings of apostlehood, except good visions which a Muslim sees
or someone is made to see for him. And see that I have been forbidden
to recite the Qur'an in the state of bowing and prostration. So far as
Ruk'u is concerned, extol in it the Great and Glorious Lord, and while
prostrating yourselves be earnest in supplication, for it is fitting
that your supplications should be answered.
حَدَّثَنَا سَعِيدُ بْنُ مَنْصُورٍ، وَأَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ
وَزُهَيْرُ بْنُ حَرْبٍ قَالُوا حَدَّثَنَا سُفْيَانُ بْنُ عُيَيْنَةَ،
أَخْبَرَنِي سُلَيْمَانُ بْنُ سُحَيْمٍ، عَنْ إِبْرَاهِيمَ بْنِ عَبْدِ
اللَّهِ بْنِ مَعْبَدٍ، عَنْ أَبِيهِ، عَنِ ابْنِ عَبَّاسٍ، قَالَ كَشَفَ
رَسُولُ اللَّهِ صلى الله عليه وسلم السِّتَارَةَ وَالنَّاسُ صُفُوفٌ
خَلْفَ أَبِي بَكْرٍ فَقَالَ " أَيُّهَا النَّاسُ إِنَّهُ لَمْ يَبْقَ
مِنْ مُبَشِّرَاتِ النُّبُوَّةِ إِلاَّ الرُّؤْيَا الصَّالِحَةُ يَرَاهَا
الْمُسْلِمُ أَوْ تُرَى لَهُ أَلاَ وَإِنِّي نُهِيتُ أَنْ أَقْرَأَ
الْقُرْآنَ رَاكِعًا أَوْ سَاجِدًا فَأَمَّا الرُّكُوعُ فَعَظِّمُوا
فِيهِ الرَّبَّ عَزَّ وَجَلَّ وَأَمَّا السُّجُودُ فَاجْتَهِدُوا فِي
الدُّعَاءِ فَقَمِنٌ أَنْ يُسْتَجَابَ لَكُمْ " .
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