A better solution is probably a raised standard of living and more education.
edit: By raised standard of living I'm not talking about AC and other energy-intensive luxuries. I mean not having to have 7 kids because many of them will probably die.
Someone, or something, will ultimately be making decisions.
Why not a government, or government analog?
What about that bothers you? What alternatives do you suggest? Different mechanisms? Different institutions?
Raising standards of livings has always required raising material resource consumption.
In the end I think the individuals themselves will be the ones making the decision to have fewer kids. I don't have a source for this, but I seem to remember that immigrants to more developed nations have fewer children after assimilating than people in their native, less developed countries.
These seem to reflect strong underlying tendencies of complex evolving systems. In particular that higher levels of organisation and complexity very powerfully tied to greater rates of energy and resource use, overall if not individually.
If humans manage to defeat this tendency it would be a singular exception.