I am guessing that this has come about over a short time period and fresh warm water is not having much affect in fully removing it?
There are a couple of underlining medical issues, which could be the source, but they tend to be rare.
If you are using newspaper or like printed paper for the bird droppings, it is very possible what you are seeing is ink transfer. Current water based ink used in near all common printing especially for newspapers is much safer than what was used in the past. However, it 'easily transfers' and will discolor surfaces that come in contact with it.
Trying using non-printed paper for the bottom of your bird cage. Non-printed 'news print' quality paper is available and commonly used to wrap glassware when shipping.
After using the non-printed paper or other non-printed products for four to six weeks; if the black areas remain, see your local avian qualified vet.