Why were slaves not allowed to sing? Or could they only sing on Sundays?

Certain songs were songs of rebellion, and some were coded... songs used to communicate. These types of songs were whispered, as punishment would occur if heard by the slave holders or plantation foremen.

Harriet does note, however, that Sundays were special because they didn't have to work in the fields. Thus, they were free to do their laundry, tell stories, and sing.