Without a picture it's very hard to determine what's going on and what disease might be present b'c there are several diseases that can result with black spots on the fruits.

Do you see any spots on the foliage? If so can you please describe them as to size and color and shape and whether they have yellow halos around them.

Perhaps it might help if you look at the TAMU
site I've linked to below and see if you make a match.

Carolyn

Here is a link that might be useful: TAMU Tomato Disorders