The African Slave trade in Central and South America actually started in the Caribbeans. Many people know that the Spanish/Portuguese were in the "Americas" for "Gold, Glory & God". This holds true in this circumstance as well.
Upon discovering the island of Hispanola (which is today Haiti/Dominican Republic), Christopher Columbus brought over Sugar Cane on his second trip. They needed people to grow the sugar can though and this is where the problems began. Originally they began to use the Hispanola natives as slaves to cultivate the sugar cane crops, but there were two major problems with this: 1. The Hispanolas were not physically capable of withstanding slave conditions and 2. the Spanish/Portuguese missionaries wanted to convert them to Christianity. The later could not effectively be done if they were enslaving the people for the people would want to know why this new "God" would treat them like this.
Then the Portuguese came up with an idea. Why not take the African slaves they were already using in parts of Europe and send them to the Caribbeans. The African slaves were stronger and could withstand more work/abuse then the Hispanolas and the missionaries could have their converts.
Everyone would be happy!
And that's were African slavery and Central and South America came from. From the Caribbeans it spread out into Central and South American (both of which were highly populated and owned by the Spanish and Portuguese).