Hm. Maybe the most effective way of reducing abortions (including infanticide or abandonment) would be to make contracpetion encouraged for people under 25, and forbidden for people over 25. The idea being, young people some of whom who are likely to end up having sex anyway will get contraception, but older people who are more likely to actually abstain if denied effective contraception will be forced to do so.

Of course, you could pick another cut-off than age, but I think either way it's a awfully unacceptable idea.