It sounds like septoria leaf spot which is a fungus. It would help to see a photo. Try removing the leaves with spots and use a fungicide. You also might want to clean up underneath the plant and make sure there are no weeds around it. If you are growing your plants crowded you should consider allowing room between them for air circulation. Please post a photo though to be sure. I'm sure someone here can verify the problem.

SEPTORIA LEAF SPOT OF RUDBECKIA
The fungus Septoria rudbeckiae is one of the most common foliar pathogens of Rudbeckia (Figure 1).

Symptoms
Symptoms begin as small, dark brown lesions that enlarge from 1/8 to 1/4 inch in diameter. Although the lesions are usually rounded, there may be angles where leaf veins limit the spread of the fungus (Fig. 2). Symptoms of this disease may be difficult to distinguish from those of angular leaf spot of Rudbeckia.

Signs
Microscopic examination of the lesion will reveal black, flask-shaped structures called pycnidia that contain thousands of thread-like spores. Spores are produced in late spring and early summer, causing leaf spots on the lower leaves. The spores of the fungus are dispersed by splashing water, with lesions first appearing on lower leaves and later developing on upper leaves as the season progresses.

Management
To manage this disease, remove the infected leaves at the end of the growing season to reduce inoculum levels. Because leaf moisture is essential for infection to occur, increase air circulation around the foliage by properly spacing plants (and removing volunteer seedlings) to prevent over-crowding. As with other foliar disease problems, avoid overhead watering. Fungicides containing chlorothalonil or copper* may protect new growth and reduce the spread of the disease. Preventative applications of fungicides should begin in early to mid June prior to the onset of symptoms.

CYLINDROSPORIUM AND RAMULARIA LEAF SPOT OF RUDBECKIA

Ramularia rudbeckiae and Cylindrocladium spp. have been reported as causing leaf spots on members of the genus Rudbeckia (Fig. 3).

Symptoms
Development of this disease is rarely as severe as Septoria leaf spot. Symptoms include small, scattered lesions that are often angular in appearance.

Signs
Microscopic identification of the acervulus (in the case of Cylindrocladium) or conidia and conidiophores (for Ramularia sp.) is required to distinguish from Septoria leaf spot.

Management
Like Septoria leaf spot, frequent watering (due to rainfall or irrigation) that results in leaves that are wet for extended periods favors these diseases. Control consists of proper watering so that leaves are not wet for extended periods. Management is the same as for Septoria leaf spot.

Here is a link that might be useful: Diseases of Rudbeckia