I had this problem, didn't read into the problem of black limestone before filling in the cracks with Mortar.
I have managed to removed 90% of the stains by a combination of Karcher and scrubbing with a little bit of 'pink stuff' cleaner. Then applied LTP external stone sealer (water based).
Don't mind me while I bump up some older but good threads. If you can contribute to the thread, go ahead. But if it's nothing for you then don't reply and it'll soon drop off the What's New page etc.
Worth linking to our new forum structure while I'm doing stuff:-