ScrollRectHolder holds ScrollRect component. The content of it is ScrollContent. Add Vertical Layout Group component on ScrollContent. It's also the parent of the buttons that will be instantiated each time you need. Button is the button prefab that will be instantiated. The variable initialHeight is the initial height of ScrollContent. Have to get it from Rect Transform of ScrollContent. Need to update sizeDelta with adding initialHeight whenever you add a new button.

public void AddNewButton()
{
 mRect.sizeDelta = new Vector2(mRect.sizeDelta.x, mRect.sizeDelta.y + initialHeight);
 GameObject gO = Instantiate(buttonPrefab);
 gO.transform.parent = transform;
}

ScrollRectHolder holds ScrollRect component. The content of it is ScrollContent. Add Vertical Layout Group component on ScrollContent. It's also the parent of the buttons that will be instantiated each time you need. Button is the button prefab that will be instantiated. The variable initialHeight is the initial height of ScrollContent. Have to get it from Rect Transform of ScrollContent. Need to update sizeDelta with adding initialHeight whenever you add a new button.

public void AddNewButton()
{
 mRect.sizeDelta = new Vector2(mRect.sizeDelta.x, mRect.sizeDelta.y + initialHeight);
 GameObject gO = Instantiate(buttonPrefab);
 gO.transform.parent = transform;
}

unitypackage with scene, script and prefab. Unity 5.2.4f1.

ScrollRectHolder holds ScrollRect component. The content of it is ScrollContent. Add Vertical Layout Group component on ScrollContent. It's also the parent of the buttons that will be instantiated each time you need. Button is the button prefab that will be instantiated. The variable initialHeight is the initial height of ScrollContent. Have to get it from Rect Transform of ScrollContent. Need to update sizeDelta with adding initialHeight whenever you add a new button.

public void AddNewButton()
{
 mRect.sizeDelta = new Vector2(mRect.sizeDelta.x, mRect.sizeDelta.y + initialHeight);
 GameObject gO = Instantiate(buttonPrefab);
 gO.transform.parent = transform;
}

ScrollRectHolder holds ScrollRect component. The content of it is ScrollContent. Add Vertical Layout Group component on ScrollContent. It's also the parent of the buttons that will be instantiated each time you need. Button is the button prefab that will be instantiated. The variable initialHeight is the initial height of ScrollContent. Have to get it from Rect Transform of ScrollContent. Need to update sizeDelta with adding initialHeight whenever you add a new button.

public void AddNewButton()
{
 mRect.sizeDelta = new Vector2(mRect.sizeDelta.x, mRect.sizeDelta.y + initialHeight);
 GameObject gO = Instantiate(buttonPrefab);
 gO.transform.parent = transform;
}