Even if it were possible or ethical to outlaw abortion, this wouldn’t prevent abortions from taking place. Desperate people do desperate things, often involving secret clinics or self-harm.
The best way I can think of to actually prevent abortions is to allow birth mothers to benefit significantly from carrying a child to term and giving it up for adoption. That is, each interested prospective family would put in a bid (and the birth mother can set a minimum) to cover what we’ll call an adoption fee. Perhaps the birth mother can include information like DNA analysis for both her and the father, biographical details, SAT scores, etc and this would encourage prospective adopters to bid higher.
This is a great start-up idea. eBay for buying babies. Of course, we’d have to be careful with our diction because selling babies is illegal and all that. But adoption fees aren’t! Okay, let’s get to work. Maybe we can finally make everybody happy: couples who can’t have children but can pay, pro-lifers and women who aren’t ready for a baby.