Could be a rot, Cladosporium Fruit Rot, have a look and see if they are really black or if its a dull dark green.
Other than that, it could be sooty mould, which forms on the honeydew that aphids secrete, but I haven't seen this on raspberry fruit - if you look at the leaves they would be slightly shiny and sticky if it's this. It doesn't sound like this disease.
Edited to say that: spraying with Bordeaux mixture as a preventative might help, or if it's sooty mildew, spraying the aphids off with jets of water will stop them giving off the honeydew and then there won't be any sooty mould. Increased air circulation will help all plants to withstand fungal attacks.