There is no way to make it work this way, since clientListener will work BEFORE by design.
However, you can achieve your goal just by launching your javascript request from actionListener directly.
Do something like this in the actionListener's method:
FacesContext fctx = FacesContext.getCurrentInstance();
ExtendedRenderKitService service = Service.getRenderKitService(fctx, ExtendedRenderKitService.class);
service.addScript(fctx, "showMyTable();");