I have never seen a balance that was not replaceable. I can't picture yours from the description. But the fact that you know it is a steel coil means you have some idea what it is. Almost always the balance can be removed by screws, if it is a steel wire wrapped in a spring coil,....or the springs are accessible by removing an access panel. You might have to look closely as the screws may be heavily painted over.
Some pictures would help.