Stephens was shot and killed in July 2016 after smashing up an empty police car with a weed slasher in Rotorua.
RNZ's court challenge says the coroner's ruling amounts to a blanket suppression order over the inquiry, which is inconsistent with the principles of open justice and freedom of expression.
The media organisation also said public scrutiny was vital, given the significant discrepancies it had uncovered in the case.
Ryan banned reporting under section 74 of the Coroners Act. He set out the reasons for his decision in a coroner's minute.
RNZ requested the minute but was only given an extract. Even that document is subject to the non-publication order so RNZ cannot tell the public what the coroner's reasons are.
Stephens' whānau have been fighting for a full inquest into his death but the coroner has said only a narrow inquest is needed because the IPCA had already established much of what happened on the day Stephens was shot.
On June 30, after RNZ's investigation, the IPCA announced it would reopen its inquiry. Principal operations adviser Warren Young said after an initial review the authority had decided to take "a more indepth review of our original investigation".
The review is expected to be completed by the end of October.
