How bad is the problem? Have a look at the image. What stage are you at?
Most bananas are susceptible to BSD (Black Sigatoka Disease). It is extremely difficult to control. In large commercial plantations. But the costs associated with this control can be 15-20% of the final cost. Are you in a position to but chemicals? Do you want to use chemicals?
An important factor limiting disease severity is maintaining balanced nutrients. "A balanced nutrition results in high rates of leaf emergence, leading to better tolerance and possible escape from the effects of Mycosphaerella leaf spots. Banana plants are more prone to higher attack of BS in soils deficient in potassium or with unbalanced N/K relationship ." http://www.fao.org/3/a-as177e.pdf
The same article discusses nitrogen, calcium and potassium. Have you been adding fertilizer? Can you? How quickly are new leaves appearing.
Irrigation is also important. Please describe this for your fields.
Sanitation is also important. What are you doing with the infected leaves? How big is the plantation and are their nearby plantations of bananas.
Please provide answers to these questions and we will try and help. Also, please provide images.
Stages of infection by black sigatoga
Aerial application of fungicides to control black Sigatoka in Honduras. In the final analysis, the costs associated with these control measures are directly responsible for 15-20% of the purchase price of exported fruit in the importing countries. (Photo courtesy of R.H. Stover).