enum {
...

PROP_ACTIVATABLE_RELATED_ACTION,
PROP_ACTIVATABLE_USE_ACTION_APPEARANCE
}

struct _FooBarPrivate
{

  ...

  GtkAction      *action;
  gboolean        use_action_appearance;
};

...

static void foo_bar_activatable_interface_init         (GtkActivatableIface  *iface);
static void foo_bar_activatable_update                 (GtkActivatable       *activatable,
                                   GtkAction            *action,
                                   const gchar          *property_name);
static void foo_bar_activatable_sync_action_properties (GtkActivatable       *activatable,
                                   GtkAction            *action);
...


static void
foo_bar_class_init (FooBarClass *klass)
{

  ...

  g_object_class_override_property (gobject_class, PROP_ACTIVATABLE_RELATED_ACTION, "related-action");
  g_object_class_override_property (gobject_class, PROP_ACTIVATABLE_USE_ACTION_APPEARANCE, "use-action-appearance");

  ...
}


static void
foo_bar_activatable_interface_init (GtkActivatableIface  *iface)
{
  iface->update = foo_bar_activatable_update;
  iface->sync_action_properties = foo_bar_activatable_sync_action_properties;
}

... Break the reference using gtk_activatable_do_set_related_action()...

static void 
foo_bar_dispose (GObject *object)
{
  FooBar *bar = FOO_BAR (object);
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (bar);

  ...

  if (priv->action)
    {
      gtk_activatable_do_set_related_action (GTK_ACTIVATABLE (bar), NULL);
      priv->action = NULL;
    }
  G_OBJECT_CLASS (foo_bar_parent_class)->dispose (object);
}

... Handle the “related-action” and “use-action-appearance” properties ...

static void
foo_bar_set_property (GObject         *object,
                      guint            prop_id,
                      const GValue    *value,
                      GParamSpec      *pspec)
{
  FooBar *bar = FOO_BAR (object);
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (bar);

  switch (prop_id)
    {

      ...

    case PROP_ACTIVATABLE_RELATED_ACTION:
      foo_bar_set_related_action (bar, g_value_get_object (value));
      break;
    case PROP_ACTIVATABLE_USE_ACTION_APPEARANCE:
      foo_bar_set_use_action_appearance (bar, g_value_get_boolean (value));
      break;
    default:
      G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
      break;
    }
}

static void
foo_bar_get_property (GObject         *object,
                         guint            prop_id,
                         GValue          *value,
                         GParamSpec      *pspec)
{
  FooBar *bar = FOO_BAR (object);
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (bar);

  switch (prop_id)
    { 

      ...

    case PROP_ACTIVATABLE_RELATED_ACTION:
      g_value_set_object (value, priv->action);
      break;
    case PROP_ACTIVATABLE_USE_ACTION_APPEARANCE:
      g_value_set_boolean (value, priv->use_action_appearance);
      break;
    default:
      G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec);
      break;
    }
}


static void
foo_bar_set_use_action_appearance (FooBar   *bar, 
                   gboolean  use_appearance)
{
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (bar);

  if (priv->use_action_appearance != use_appearance)
    {
      priv->use_action_appearance = use_appearance;
      
      gtk_activatable_sync_action_properties (GTK_ACTIVATABLE (bar), priv->action);
    }
}

... call gtk_activatable_do_set_related_action() and then assign the action pointer, 
no need to reference the action here since gtk_activatable_do_set_related_action() already 
holds a reference here for you...
static void
foo_bar_set_related_action (FooBar    *bar, 
                GtkAction *action)
{
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (bar);

  if (priv->action == action)
    return;

  gtk_activatable_do_set_related_action (GTK_ACTIVATABLE (bar), action);

  priv->action = action;
}

... Selectively reset and update activatable depending on the use-action-appearance property ...
static void
gtk_button_activatable_sync_action_properties (GtkActivatable       *activatable,
                                          GtkAction            *action)
{
  GtkButtonPrivate *priv = GTK_BUTTON_GET_PRIVATE (activatable);

  if (!action)
    return;

  if (gtk_action_is_visible (action))
    gtk_widget_show (GTK_WIDGET (activatable));
  else
    gtk_widget_hide (GTK_WIDGET (activatable));
  
  gtk_widget_set_sensitive (GTK_WIDGET (activatable), gtk_action_is_sensitive (action));

  ...
  
  if (priv->use_action_appearance)
    {
      if (gtk_action_get_stock_id (action))
    foo_bar_set_stock (button, gtk_action_get_stock_id (action));
      else if (gtk_action_get_label (action))
    foo_bar_set_label (button, gtk_action_get_label (action));

      ...

    }
}

static void 
foo_bar_activatable_update (GtkActivatable       *activatable,
                   GtkAction            *action,
                   const gchar          *property_name)
{
  FooBarPrivate *priv = FOO_BAR_GET_PRIVATE (activatable);

  if (strcmp (property_name, "visible") == 0)
    {
      if (gtk_action_is_visible (action))
    gtk_widget_show (GTK_WIDGET (activatable));
      else
    gtk_widget_hide (GTK_WIDGET (activatable));
    }
  else if (strcmp (property_name, "sensitive") == 0)
    gtk_widget_set_sensitive (GTK_WIDGET (activatable), gtk_action_is_sensitive (action));

  ...

  if (!priv->use_action_appearance)
    return;

  if (strcmp (property_name, "stock-id") == 0)
    foo_bar_set_stock (button, gtk_action_get_stock_id (action));
  else if (strcmp (property_name, "label") == 0)
    foo_bar_set_label (button, gtk_action_get_label (action));

  ...
}