The northern tip of Zanzibar, around the village of Nungwi, sits close to some of the richest deep-sea fishing grounds on the African coast. The channel between Zanzibar and Pemba island offers good game fishing, according to an archived tour listing summarised here.
August to November. This is the time for big yellowfin tuna, among the strongest fish in the sea. Blue marlin and a number of striped and black marlin are also found, along with sailfish. During this period it is common to hook several fish at once, when large schools of tuna chase smaller fish near the surface.
November to March. This is the billfish season. Striped marlin are the most common and are sometimes seen in groups of ten. Large blue and black marlin are also frequent.
If you want a gentler day on the water, compare it with the snorkelling trip off Zanzibar.