I am so sorry for the slow response to your post :(
It appears to me that the problem is most likely a fungal problem causing the black spot symptom. Common treatments for this include copper based fungicides; I have had success with this treatment on other plants. While I have not tried it, I have also heard and read that Neem oil treatment can also be successful.
Here is a link for making your own copper based fungicide. I hope this is helpful :)