Thanks for writing. Without seeing your plants in person, I can't be sure, but it sounds like a fungal disease --- a very common problem on black-eyed Susans. Help prevent it by growing your plants in a bright, sunny spot (shade makes them more susceptible to the disease). Also: Avoid watering the plants with a sprinkler; wet leaves can also encourage the disease.
If that doesn't help, you can try spraying them with a fungicide, or look for a variety next year that's better suited to your conditions so it won't succumb to disease as easily.
---Justin, Senior Garden Editor, BHG.com