thats normal. When you do the Depo shot most females will not get a period and will get spotting. the dark discharge is just old blod that is still shedding.
I would talk to your doctor, just in case. I have never had the depo shot, but I had a friend who had it. While she did have the spotting, it didn't go so far as to continue until 2 months later. Call or go in to see your doctor, and see what they say. Its always better to be safe than sorry.
Probably just a side effect from the depo. At least your not bleeding constantly like I did