Welcome to the 21st century! What you want to do is locate all four valves, and replace them with electric ones. That is where the industry is nowadays. If it happens that the old valves are brass-with-plastic then you might be able to fit a new adapter to the brass part, but for the money, it's cheaper to start over. If you had complete confidence in the (no longer manufactured) hydraulic controller, you could still get Toro hydraulic valves to substitute for the originals. (try Toro part number 250-00-04)
Two caveats. If you are in lightning territory, like Florida, hydraulic controls still have their place. Second, it is likely that there is no backflow protection in that old sprinkler system, and you do want to take care of that oversight.