There is a lot of literature out there on the morality surrounding procreation. It usually focuses on the extent to which parents can have duties not to procreate given certain likely facts about the child that would be born, or given certain facts about the capacity of the parents to care for it.
Obviously every thread has a life of its own and can end up in all sorts of places, but I'd like to begin by asking readers to consider one particular kind of decision when it comes to procreation – specifically the decision whether one ought to adopt rather than procreate at all.
I have in mind here both cases where you have a fertile couple who are perfectly suitable to be parents (however you want to flesh that out) as well as cases where you have an infertile or same-sex couple considering having a child via surrogacy or some other expensive method.
Of course there are practical reasons why adoption might not be an option for some of these couples, but we can set those cases to one side for the purpose of this discussion. Assuming no legal or other practical impediments, and assuming that in the case of infertile couples financially speaking it will be more costly to conceive a child than to adopt one, the only reason I can think of why one might not want to adopt is that we have a preference for raising a child who is genetically-related to us.
The question then seems to turn upon whether this preference is the sort of preference we can legitimately act upon by choosing procreation over adoption – whether we can use it to justify adding another person to an overpopulated world while also depriving an already-existing child of the upbringing they would otherwise have received.
The strongest way of putting this argument is to say that the genetic factor is merely a fetish on our part and one we ought to overcome in favour of the greater good of providing a home to an already-existing child who needs one.
Two caveats before I finish:
First, the question posed is not necessarily about what laws we ought to have. There are lots of reasons why it wouldn't be a good idea to enforce a moral obligation to adopt, even if such an obligation exists. But these would be pragmatic, practical reasons, rather than principled ones, if there is a moral obligation to adopt.
Second, the question does not assume that people are obliged to go out and adopt, even if they don't want children in the first place (although that's not ruled out by what I've said here). Rather, the question only applies *if* a couple decide they want to raise children at all. *Then*, so the argument goes, provided that certain conditions are met (that there are children in need of homes, that it's not impractical or illegal etc.) they have a moral obligation to adopt rather than procreate.