Probably a slight adjustment of the Horiz stabilizer coil would center the horizontal hold, however you say it's shaky in any case so possibly the horizontal AFC diode is bad, at least I would guess a set of that vintage uses a solid state diode, actually two diodes in one package in most cases.
They are usually a small rectangular plastic component with three legs.
Like these.
http://www.ebay.com/itm/Qty-2-ECG-11...item1e9d2e8169