Tikopia, a Polynesian island is probably the best example.
http://en.wikipedia.org/wiki/Tikopia
The effect of European influence upon Tikopia was less than positive. The British colonial govenment of the Solomon Islands forbade warfare, while Christian missionaries preached against abortion, infanticide and suicide.
The Tikopian population grew by half again, in less than 30 years, until it was nearly wiped out by famine caused by two cyclones in successive years.
The New Guinea highlands are another example. When Europeans penetrated the jungle, they were surprised to find an agrarian society in the countries' interior. This is a society that has maintained itself for at least 7,000, using self-developed farming techniques that work when European attempts to "improve" things have failed.
They limited their population through war, infanticide, use of forest plants for contraception and abortion, and sexual abstinance and natural lactational amenorrhea for several years while a baby was being nursed.
