"There are many countries in South America."
Translation:Det ligger många länder i Sydamerika.
Yes, Sydamerika is a name, a proper noun, so saying södra Amerika for it would be like saying southern Africa for the country South Africa in English. Do note that if the English sentence had said "south America" with a lowercase "s", it would not have referred to the proper noun, and your translation would have been the correct one.
det är in this kind of context typically indicates a less permanent existence, so it's not generally suitable for things like countries.
That said, it can be perfectly fine colloquially.