I would not advocate this authoritarian approach (I'm not saying you are). Part of the solution is what you said earlier, education. But population stabilizes on it's own as a country goes through the Demographic Transition.
See: https://en.wikipedia.org/wiki/Demographic_transition
Or for something more light-hearted: https://www.youtube.com/watch?v=QsBT5EQt348
We need to empower women in those countries and enable people to make a living in other ways than selling timber and slash-and-burn agriculture. Breeding and selling rare butterflies[1] is one option that I've heard of, but obviously that doesn't scale. I don't find it unreasonable to just pay people for not cutting down rain forests. First world countries have a responsibility here. After all we cut down all our old growth forests and now demand that developing countries don't do the same.
[1] https://www.reuters.com/article/us-kenya-butterflies/kenyans...
We need to realise that sometimes the "authoritarian approach" is the only option available. There is no other way to put the brakes on steep population growth especially as this is usually linked to culture and education. But education may work 20 years down the line, which is too late for such an issue.
The demographic transition is also besides the point as the issue is to stabilise population at a lower level that it would have done 'naturally'.
> fertility decline in Africa has generally proceeded more slowly than in other parts of the world, with several cases of “stalls” and even small fertility increases over time
https://openknowledge.worldbank.org/bitstream/handle/10986/2...
> While this study looks at lessons from East Asia, Latin America, and the Middle East, Sub-Saharan Africa currently exhibits two unique demographic characteristics. First, it is the only region in the world that is still at a very early stage of the demographic transition. As such, it can learn from other regions that have gone through the same journey to ensure that demographic change paves the way to deeper and more sustainable prosperity. As this book points out, this path is neither easy nor automatic. Success requires actions in differ- ent policy realms that are time-coordinated, adapted to the current level of the demographic transition, and results-driven. The second unique characteristic of the region’s demographic picture is its heterogeneity. While a small number of countries are far along the transition, with fertility rates that are below replacement levels, many others are exhibit- ing surprising delays in the transition in the last 10 years. Some countries are showing very little movement along the natural transition and are stuck at very high fertility rates. These large differences argue for differentiated policies that target different sectors and processes. They also argue for country to country learning and knowledge sharing.