Back when 3 wire feeders were permitted a "Sub Panel" was treated the same as the "Service Panel" at your residence. At the Sub Panel the Neutral and ground were bonded at the panel and a ground rod was installed at the Sub Panel location. So to get this back the way it was probably originally wired then from the 3 wire feeder connect the Blk & Red wires to your "Hot Lugs" at the Sub Panel as they were intended to be your Hot wires. Connect the Neutral wire from the feed to Bus bar and "bond" the Bus Bar to the casing of the Sub Panel. This is commonly done with a "Green Screw" that are supplied with the Panels. You may need to go purchase one. The bare copper ground coming from the conduit is already connect to the panel so after installing the Green Screw you could just leave it where it's at or move it to the Bus Bar. You will also want to drive a Ground Rod at the Sub Panel and connect it to to Bus Bar. That's how it was originally intended.

or you can run a Ground from the Service Panel to the Sub Panel and not put a Green Screw (not Bond the Sub Panel) and keep all Neutrals and Grounds Separate but still add the Ground Rod.

But if it was me, I would just redo it and use a 4 wire feeder and bring it all up to current Code, as there are several things that need to be changed. If not and something happens your SOL especially if a non Licensees person touches it.