Ask Mr. Smarty Plants

The black stuff on your  Rudbeckia hirta (blackeyed Susan) is likely honeydew, excreted by aphids (most frequent culprit), whiteflies or mealy bugs. The honeydew is a sticky substance, usually on the underside of leaves. and it in turn becomes a host for sooty mold fungus. As with any fungus, the first line of defense is cultural. Don't use overhead watering on the plants. water early in the day so the leaves can dry out before sundown. Pick up and destroy infected leaves, both on the ground and on the plant. If the whole plant has been affected, even though the sooty mold will not probably kill it, you might consider destroying that whole plant to cut out one step in the infection of other plants.  Space your plants far enough apart for good air circulation, and make sure they are getting plenty of sun, both enemies of fungi.

Next, you want to get at the insects that cause the excretions. Don't use insecticides, because they will most likely kill the benign, natural predators of the insects, like ladybugs. Also, if your flowers are attracting butterflies or bees, you don't want to hurt them, either. This University of California Integrated Pest Management website Aphids covers some of the management practices for aphids, which will also apply to the other insects. A good hard spray of water (remember, early in the day) to the undersides of the leaves will usually dislodge the bugs and they won't be able to get back up.

One other possibility, somewhat more dire, is Verticillium Wilt. This University of Illinois explains that it is a soil-borne fungus, and there is no cure. If you determine that is the problem, we would suggest the immediate removal of the affected plant, especially since blackeyed Susans are usually annuals or biennials and easily replaced. And keep your eye out for any other plants exhibiting the same symptoms, removing them also.