Engaging as ever, Hans Rosling presents a baseline understanding of population dynamics to the end of the century.
As he presents it, infant mortality and two surviving children per household are the universal determining factors for reaching a stable replacement rate.
What he implies is perhaps more interesting: that the behavior is reversible, and that a rise in infant mortality due to failed health care, war, or famine caused by GW would trigger the return of large family sizes -another secondary positive feedback.
With a TFR (total fertility rate) of 2.+ we reach a sable population, but what's really needed is a number closer to 1.7 for a drop after the peak. He doesn't address that here specifically, but it is implied by his examples of falling local populations is that it occurs when women are fully engaged in the economic life of the culture -and not necessarily getting wealthy or having a high carbon footprint, just being full participants.