In a previous post, I said that an outright prohibition on birth would be a moral horror, because given our current level of technology, it would mean forced abortion, forced sterilization, or both. While a pure consequentialist might still argue that the harm of later generations being born might outweigh the extra suffering a "forced abortion generation" had to undergo, there are strong agent-relative reasons to not forcibly perform abortions, even though by not doing so, we allow a greater violation of rights to occur.
In attempting to formulate an example to illustrate this, I noticed that all the examples in the anti-consequentialist literature (people like Thomas Nagel and Bernard Williams) feature an agent faced with a choice of harming someone himself, or having someone other than his possible victim do much greater harm. The antinatalist forced abortion dilemma is different: one would be faced with a choice of harming someone, or allowing that person to do harm to another person. The forced abortion case has a great deal more in common, perhaps, with defense-of-others cases than the typical anti-consequentialist examples. (It should give us pause, however, that anti-abortion fanatics follow this same logic to the conclusion that it's morally appropriate to shoot abortion doctors.)
There is an alternate political possibility to forced abortion and forced sterilization: creating an incentive structure that provides negative incentives for birth and positive incentives for not procreating (and which, one would hope, would legitimize refusing to give birth and remove some of the social and moral legitimacy of voluntary procreation.) But both an outright ban and an incentive structure suffer from the same problems as those in place to curb prostitution and drugs.
Anti-prostitution laws exist for a variety of reasons, but the most common justification in our modern era is that they exist to protect women who are or would become prostitutes from exploitation. The problem with anti-prostitution laws is that they universally seem to do greater harm to the very class of people they're intended to protect - prostitute women. It is impossible to imagine an anti-prostitution law that would not harm prostitutes. Even laws that provide for prosecution of prostitutes' customers only, and not the prostitutes themselves, drive traffic underground and thereby make it much less safe for prostitute women.
Anti-drug laws are, in theory, motivated by a desire to minimize harm to people, including drug users and those otherwise affected by the drug trade, such as those whom drug users might steal from to support their habits. But a consensus seems to be developing among economists and social scientists that the drug prohibition does more harm than it prevents - to the very people it is intended to protect.
Birth seems to have in common with prostitution and drugs the status of being a good with inelastic, or close to inelastic, demand, especially for the first child. China's one-child policy has had some success, though there are reports that it functions both as an incentive structure and as an outright ban (I can't figure out if reports of forced abortion are reliable). But the one-child policy is not an antinatalist policy but a limited procreation policy. There is reason to believe that increasing the cost of procreation in an attempt to drive procreation to zero - either through a sort of tax structure, or through positive incentives for non-procreation - would fail miserably, and, as with prostitution and drugs, would harm the very people the policy was intended to protect. Any incentive against procreation (a) would likely not significantly reduce procreation, since, based as it is in a strong biological drive, some level of procreation likely has near-inelastic demand (and supply is hard to control); and (b) would necessarily harm the children who were nonetheless brought into existence.
For example, let's say procreation now carries a $10,000 fine or 6 months in jail if the fine is not paid. Most people would likely procreate anyway, and either pay the fine or serve the jail sentence. And a child brought into the world would be faced with parents who have either $10,000 less to spend on his upbringing, or 6 months less time to work to save money for the child's upbringing.
I think there is one possible hope: incentives for voluntary, permanent sterilization. While, at some point, the majority of humans seem to want to procreate, humans have a notoriously high discount rate. If a great enough incentive were offered early enough in life, many might accept the incentive and be permanently sterilized; while they might regret the decision later, their children and grandchildren would never exist, and would therefore never have reason to regret their lives.