now this gets me wondering, did white people back then try to control the reproductive rights of black people (or even kill black children or force black couples into aborting their children) to achieve this goal?

I don't know about doing it on purpose, but the Tuskegee syphilis experiment comes to mind as one of the ways the result was that. You can also argue that condemning black people to poverty and misery through policing the black body (by segregation, white terrorism, objectification, etc.) is a way to make sure they weren't able to exercise their reproductive rights freely. Really hard to have a fulfilled family life when everything you've ever known regarding your own body is brutalization.