We know the best (and really the only effective) way of lowering birth rates is to increase the wealth of the population.
Increased wealth pretty much straight away leads to better spending on maternal and infant healthcare, which means lower maternal and infant mortality and less babies need to be born (families don't over-procreate to cover some of their children dying before adulthood). And richer populations mean more middle class service workers, which means a reversal in the cost-benefit of having more children (when you're a poor subsistence farmer, more children means more help in the family business so you have more; now more children means more cost in providing for them and their education).
So by helping the poor be not poor you reduce birth rates so fight climate change. It's a win win.