The Jesuit Reductions
The cities all had the same basic structures, with a central church, a school, a cemetery, areas for crops, and many community houses. In these cities, there were no social classes, no king, no slaves, and no beggars. According to the Jesuits, this was the model of society God wanted man to follow. Everyone had their place and function. All tools, seed, and animals were owned in common. Everyone would work a certain number of days as a kind of payment to the common good. As a theocracy, there were no real kings or leaders. Everything was decided by the Jesuit priests and the native elders. All the indigenous people were catechized. They were educated in both basic literacy and in the arts, especially music, sculpture, and even ironcraft. There was also training in the care of children, making clothes, medicine, animal husbandry, and, most significantly, civil defense.

Plan of the Reduction of San Juan Bautista, c. 1756
The slavers knew that their success rested on their ability to overwhelm the indigenous people--who were previously living a nomadic life in the rain forest--with advanced weaponry. But the Jesuits gathered these scattered tribes together, raised these small cities with them, and taught them to defend themselves. The slavers saw a great dropoff in the success of their enterprise; no longer could four men with muskets capture fifty natives to be sold in Sao Paulo or Buenos Aires, because the natives fought back. Essentially, the Jesuits armed the indigenous people and turned them into an effective fighting force.
Between 1750 and 1770, Spain and Portugal, whose economies both relied on slavery, signed a series of treaties which effectively declared the Reductions illegal. As they had created such a threat to European economic stability, the Jesuits found themselves with many enemies. The royal houses of Europe, and even other religious orders (especially the Dominicans, the Franciscans, and the Augustinians) convinced the Pope to disband the order in 1767. At that time there were a little over 2,000 Jesuits in South America, who had over 700,000 natives in the Reductions.
When the Jesuit order was suppressed, Jesuits were expelled from every European country and colony, and all their assets were confiscated. The Reductions were declared illegal, and the natives ordered to return to their forests. The slavers then came back to the Reductions. The natives fought as well as they could, but in the end their cities were sacked and burned. The few natives who didn't return to the forest were enslaved or murdered. By the time the Order was restored, in 1814, the Reductions were in ruins, the indigenous tribes scattered and diminished.
Other sites on the Jesuits:
The Jesuits, in their own words
Seven Things You Need to Know About the Jesuits
Jesuit Colleges and Universities in the U.S.