IMO, the best solution to overpopulation is to develop science and space technology far enough along so those of us who want to can just leave this planet before everyone blows each other up.
Seriously, we should be having colonies in space, on the moon, on Mars by now.
(Yes, not realistically, but we can do it eventually.)
And whether or not you believe in overpopulation, sooner or later, Earth will reach maximum sustainable population. Whether its 9 billion or 19 billion people, eventually there will be too many mouths to feed and not enough land to grow the crops needed to feed those people.