I am most familiar with the case of Peru, so this answer will focus on that. Having said that, the Viceroyalty of Peru was arguably the most valuable part of Spanish South America, since it included both the old Inca heartlands and the mines of Potosi.

The Spanish did bring some African slaves to Peru. However, the political and environmental conditions were quite different from Brazil. Politically, Peru had relatively complex political institutions by the time of the Spanish conquests, due to its dense population and the Inca Empire. There was an established local nobility, large-scale infrastructure projects and a system of mandatory public service (the "mita"). When the Spanish took over, rather than abolish those social relations entirely, they adapted them to Spanish rule. They copied many of the Inca institutions, mixing them with some of their own, such as the infamous encomiendas (which were a bondage system for indigenous Peruvians functionally similar to slavery). In contrast, there was never such a complex political system in Brazil, which was less sparsely populated anyways, so the Portuguese had to import slaves from Africa and, to a much larger extent, create institutions from scratch there.

Environmentally, the most important areas in Peru, especially the gold mines, were located in the Andes. Since Africans were not accostumed to high altitudes, there was a very high death rate among the slaves sent to work in the Andean mines. Compared to indigenous Peruvians, who were adapted to work at high altitudes, it made no economic sense to import slaves for that purpose. Some Africans were imported to work in coastal plantations, but these plantations were never as economically dominant as the mines in the Andes. Thus, while there were some African slaves, they never outgrew the indigenous populations.

Sources:

Klaren, P. Society and Nationhood in the Andes.

Cotler, J. Clases, Estado y Nación en el Perú.

You might be interested in this thread, where /u/Legendarytubahero provides an overview of slavery in Uruguay.

The short answer is that these areas did not develop plantation agriculture to the extent that Brazil did. In Brazil, different areas developed different forms of forced labor of indigenous populations and eventually developed an unquenchable desire for African slaves, especially as the sugar industry grew. The Southern Cone did not develop major plantations. Sugar, coffee, and cacao do not grow there, and mate never really developed the international demand that necessitated cheap labor (most could be supplied by Guaraní laborers). Unlike Peru as /u/r_shimabukuro demonstrated, there were not nearly as many valuable mines, which required cheap labor. Plantation agriculture and mining were the main drivers of the slave trade during the colonial period and the era of "second slavery" in the late eighteenth and nineteenth century. Thus, far fewer slaves came.

HOWEVER! That is not to say that there were not African slaves in these areas. In fact, recent scholarship has shown that there may have been as many as 100,000 slaves brought into the Southern Cone over the course of the colonial period! Although some came on slave ships, most of them were smuggled in from Brazil via overland trade routes and inter-regional connections between Portuguese families residing in Brazil, the Banda Oriental (Uruguay), and the Río de la Plata (see Prado's Edge of Empire for a good overview of these connections). For much of the early part of the colonial period, these slaves were then marched overland to Upper Peru, where they fetched a sizable profit. They were the backbone of this trans-South American lateral movement of trade goods (and people) that drove the development of cities in what is today northern Argentina and Paraguay.

Later in the colonial period, the market for slaves really took off closer to the Atlantic. Buenos Aires and Montevideo were rapidly growing during the eighteenth century. Instead of laboring on plantations, eighteenth century African slaves primarily worked in urban areas, carrying out domestic and artesanal tasks. They worked in elite households; labored as shoemakers, tailors, blacksmiths, silversmiths, etc.; sold goods in the marketplace; and did agricultural and ranching related tasks outside the cities (moving back and forth depending on seasonal needs). As the colonial period came to an end, the growing supply of Africans caused the price of slaves to fall dramatically, which allowed more and more people to purchase a few slaves for their household, which in turn grew the slave population. Slaves came to be an integral part of the urban economy in the region (see Johnson's Workshop of Revolution, especially chapter 1). Their work gave slaves a great deal of mobility and flexibility in many cases to move about the city and develop personal skills, which they could use to save money on the side towards buying the own freedom. This is not to make it seem like domestic slavery was not cruel and terrible. Slaves continued to be abused and raped by their owners and did not have any autonomy over their bodies. But they did gain a level of agency that other African slaves did not receive.

It is only recently that slavery in these areas have become a hot topic of research; consequently, there is not a lot of scholarship on the subject. Argentina is still conceived of as a white nation. Yet, evidence for the presence and importance of Africans is hiding in plain sight in colonial documents, and it challenges the notion that these countries have always been European settler colonies. Censuses are filled with the presence of Africans, both free and enslaved. By 1810, the probably made up about a third of the city...perhaps more. African churches offered services, and processions regularly passed through the streets of cities in the region. Art that shows colonial Buenos Aires includes the presence of many people of African descent. Thousands of African militia fought off the British during their attempted invasion of the region. The independence armies that crossed the Andes included huge numbers of African slaves and free people. Unfortunately, the importance of Africans has largely been forgotten, overshadowed by a much larger wave of European immigration during the late nineteenth and twentieth centuries.