All inspected merchant vessel (including civilian manned US Army transport) masters are/were required to file discharge certificates with the USCG in Washington DC. They did this during wartime as well as in peacetime. If you are certain that the ship’s name was COMET then it is possible to have them search for all vessels under the US flag with that name. If there are more then you will then be able to search which of the COMETs was sailing in the waters which corresponded with your dad’s service or corresponds with the build date for the ship. Then you should be able to find those discharge certificates which should include your father’s name.
I cannot point you at the exact website for the right office at the USCG but you can go here to start.