Raise people's standard of living and you don't need vicious policy to lower birth rates.  Vietnam's has been radically decreased as the people become more prosperous.  The government has done nothing (of course contraception and abortion are available here, as part of being a secular state, but people who need them pay for them, not the government).

In particular, giving women the ability to decide when and how many children to have, and squashing those men who see it in egoist terms, brings down birth rates remarkably.  Women have more sense about these things and, of course, are the ones who have to go through the pregnancy.

What can happen, though, if population growth slows too fast is that you get an aged population and not enough young people to support them properly.  This is going to happen in China because of its foolishness here, and probably much of Europe and of course is happening in Japan -- that is what is behind its lack of economic growth now.