Business management is a very broad topic, so you are wise to be considering narrowing your research to a particular area of management. Your first step might be to do some general research on management principles, something that you should be able to do largely through an academic database such as EBSCO, which is available free to students at most colleges and universities. You will also want to consider other general aspects of childcare management, principles of child development and education because management in this sector requires an understanding of both. ERIC is a good database for that exploration, and it, too, is available through most schools.
Once you have a handle on these general areas, you can begin to look at childcare management in particular, and explore the ways in which management, educational, and developmental theories apply to this area. Not being all that familiar with childcare management in particular, I do not know how much published research is out there, but research can also be interviewing people in this field or visiting childcare centers to observe.
Certain themes should begin to emerge for you. For example, are there differences in for-profit and non-profit childcare management? To what degree does government regulation affect management of this enterprise? Can a generalist properly manage a childcare facility, or does one need to be grounded in education and/or psychology to do this more effectively? How can one assess the success of one's management of a childcare facillity? What does quality control mean when one is caring for children?
This is an interesting area for exploration, one in which you should find ample resources on general principles, at the very least, and then be able to see these principles applied in action.