Are superogatory prayers made loudly or softly?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
As for the Nawafil (supererogatory prayers) it is a Sunnah to read in them softly if they are performed during daytime unless there is a special reason for reading in them loudly.
However the Nawafil that are performed during nighttime could be done loudly or softly. The person has the choice in this matter. The evidence for this is the Hadith reported from Aisha () that she was asked: "How did the Prophet use to perform Nawafil at night?" She said: "Sometimes he would read softly, other times he would read loudly".

Allah knows best.