Here is a conundrum for you: Research shows that an increase in quality of life is inversely proportional to a drop in birth rate. Fossil fuels are also the cheapest and easiest way for poor countries to develop their economies.
So if you are truly interested in stopping population growth the solution is rather simplistic from a carbon budget perspective. Meaning: rich countries need to drastically reduce their carbon emissions (read: 10% per annum starting now) while developing countries have a window of maybe 10 years where they can still increase their carbon emissions. After that they too have to start reducing emissions (you can think of a scheme where the reduction rate increases each year).
Put more bluntly: Whenever you take a long haul flight you directly rob a child in Africa from using fossil fuels to better his or her life.