Although listed as synonyms, they are used differently. *Darkness* means dark or the absence of light. For example:

> Light shone in the darkness. 

It's unidiomatic to say *light shone in the blackness*, unless it's something metaphorical.

In addition, darkness means *night* or *evil*.

> As darkness fell, we started packing.(night)
>
> The forces of darkness took over the jungle. (evil, magic, etc.) 

Would be strange or would convey different meaning to say:

> As blackness fell, we started packing.
>
> The forces of blackness took over the jungle.

These are not wrong, but they don't seem idiomatic to me.

*Blackness* in general means the opposite of white color or whiteness(as in your case). So you could say:

> Black coffee, hair, etc. or the blackness of the coffee, hair, etc.

Or

> Dark coffee, dark hair, etc.