I do not have any black ancestry, but some of my DNA matches do, and I have spent considerable time trying to figure out how I am related to them.
I think you will be disappointed if you start out by trying to search slave schedules. As I recall, they often only list the gender and age of slaves, not their names.
What I suggest is that you try to trace your known ancestors back step by step. Investigate every record. When you get back to pre-Emancipation, you will need something to go on.
If you haven't pursued all your DNA matches, that could yield something.
As for people being marked mulatto or black on the census, in my experience it is not reliable (a clue, though) and one person may have many different racial identities over his lifetime.
WikiTree has some resources for researching slave ancestors. You might start with this:
I hope someone more knowledgeable will come along and see this thread. Meanwhile, if I can help, please send me a private message and I will see what else I can dig up. it's been a while since I worked on these issues.