How ISLAM spread in Africa:

Those are two different thesis papers waiting to be written.

If one simply looks at Africa as a land mass, then it could be said that Islam first arrived in Africa peacefully when the first Muslim refugees sought refuge in Abyssinia from Makkan oppression.

The first diplomatic contact between the Prophet (saaw) as a ruler and the Egyptian ruler occurred after the treaty of Hudaibiyah.  However, apparently Egypt then was still a province of the Roman empire, and therefore the Roman response to diplomacy shaped the Muslim relations with Egypt. Since Roman emperior Heraclius chose to side with the Ghassani Christian king who killed the Muslim emissary and arbitrarily declared war on the Islamic state, then Egypt too was cast as a subordinate province of Rome and was at war with the Islamic state.

In contrast, the Abyssinian Christian kingdom never sided with the Romans, allowing for it to sign a peace pact with the Islamic state which lasted for centuries.

Eventually, as the Muslim armies under khalif Umar (rah) defeated the Persians and then the Romans, Egypt was liberated. And since most of north Africa had Roman ties, alliances, or connections (even only loosely) and they failed to distinguish themselves from Rome's treachery, they too were at war with the Islamic state. 

After the liberation of North Africa, trade spread Islam throughout the Pan Sahel, East Africa, and into West Africa. Sometimes it was slave trade, but most trade was normal goods, textiles, minerals, dyes, etc.

In natural business relations, Muslims carried da`wah. And the leaders of the Muslims, the khulafa and wulaa, intentionally sought and encouraged Muslim businessmen of excellent character to advance trade with new regions as dawah carriers. This is documented. 

And Allah knows best.....