What documents do I need to show to a court to change the way my son's money is being invested with the bank?

Your question does not provide sufficient facts to properly respond. Are the funds being held in Minor's custodial account? Are they subject to a guardianship proceeding? If part of a Guardianship estate, is the bank the guardian or someone else? There are prudent investor rules that the fiduciary responsible for investment must follow. These rules guide investment depending upon the amount of the available investment and how often the principal must be used to support the needs of the minor. The first step is to meet with the fiduciary responsible for the investments and have them explain their position regarding available investments and the risks of alternative investments. You should then meet with an attorney to develop an alternate investment strategy that satisfies risk parameters while giving the minor child increased benefits.

Frankly not much - the court will not let you put it into the stock market. Unless you can find a higher rate at a bank or other financial institution with FDIC coverage, you are stuck.