I recently took part in a debate on Amazon about Parenting and more specifically about whether to have kids and if so, how many. It was an interesting debate with many different turns and side issues and was sometimes quite heated with some participants deciding to no longer participate.
It is an emotional issue for so many people. Through nature, we are drawn to having children - it is one of our most basic instincts. But, in modern society we finally have a choice. We can decide to have children or not and it doesn't limit our desire and need for intimacy and sex. We also can now try to balance the root desire for children with our ability to support them and the appropriateness of having more children in an already crowded world (see world population counter).
Unfortunately, the people willing to strike this balance and who consider the choice of having children against the bigger picture (world over population, global warming, financial stability, etc.) are the very people who would best serve humankind by having children. I once wrote a lengthy paper on The De-Evolution of the Human Race that included research on the sinking intelligence and abilities of humanity in western civilization because of the propensity for the middle and upper classes to not reproduce at will and the lower classes to ignore the choice. Unfortunately, there hasn't been enough years of this potential de-evolution to substantiate the idea. There has also been general increase in apparent intelligence and capability (or productivity) because of new technologies like the Internet that introduce free and easily available information to the masses. But, look around and you will see many capable, successful people who are unwilling or at least hesitant to have children. On the other side are people like the woman who rented a house of mine at one point and told me that her job was to make babies for the state - and indeed, she was getting paid more each time she had another baby. She didn't care who the father was and she was on number nine at the time.
So, in the debate on Amazon, I argued that anyone asking the question of whether or not to have children is already likely to be a better parent, a better provider, and someone who would produce better citizens than the average person out there having children. That argument started the first firestorm. It was interesting to see the reactions - they were emotional and heartfelt, but few had any logic or reasoning behind them and I stood my ground as there was nothing in the arguments to counter what I was saying.
Then the discussion turned to only-children (one child in a family) and again I started a firestorm, this one probably more deserved. I have observed many families and parenting situations (part of my research into writing Humanism for Parents - Parenting without Religion and found many parents that mistakenly enable their children - in other words give them what they want to quiet them down. Sometimes this is done as part of an (IMO invalid) parenting philosophy, but more often it is because they struggle with conflict and the personal will power it takes to stand up to a screaming child. In multi-children families where the parents tend to enable, the children end up learning that they can't always get there way. In single-child families, the child really is the center of the universe. In childhood s/he almost always gets his/her way. Then, later in life it is difficult for them to be happy because they never can get back to that situation where they get whatever they want. It makes for an adult who is difficult to please and struggles to be happy.
Of course all of the people in the debate who were only-children vehemently objected. They believed they had turned out fine thereby disproving my arguments. Of course my arguments were never about a single person and they shouldn't have taken it so personally. Also, any person tends to think s/he is "ok" (turned out well), it is an attribute of human psychology. There also hasn't been (to my knowledge) impartial studies on this, so it is difficult to prove. But it does make a lot of sense.
On the other hand, anyone who is thinking about having children and actually spending time trying to decide is much more likely to parent a single child better than those who just have children without deciding to. Again, don't take any one case and object to this - it is a blanket statement that can't be applied to a specific situation.
This isn't exactly a Humanist issue, but you can try to look at it from a Humanist standpoint. In that case we would use logic, reasoning and compassion to explore the ideas for validity (and leave emotion and reaction aside). In this case, however, I don't know of any applicable research. Maybe it is time for a graduate student or team to do just such a research project.