Is it permissible to recite the Qur'an during prostration in supererogatory prayers?

Bowing (Ruku') and prostration (Sujud) are not places for reciting the Quran, and doing so is disliked (makruh). There is no difference between obligatory (fard) and voluntary (nafl) prayers, unless it is done with the intention of supplication (du'a), such as supplicating with a verse from the Quran. In that case, there is no harm in it, whether in voluntary or other prayers.