The oath of Amanah means to say "By Amanah" as one says "By Allah". This is prohibited for the reason that one can take the oath of Allah or any of His Attributes. Amanah is one of the Commandments of Allah and an obligation prescribed by Him, like Salat, Saum, Hajj etc. In this way, the Commandments of Allah assume the resemblance of His Glorious Names and Attributes, which is not correct.