I am not an expert, but if your family has old family bibles (or even just older members who can supply you with names, places of birth, death, etc.) you can try tracking them through archives of the towns, counties, etc. where they lived and died. With some slaves in the mix, it can be a little harder to track people, but not impossible. Actually, pretty good records were kept of slaves bought, when, where and often, you may find they arrived at so and so port city on so and so date--it may even include information as to what part of the world the slaves came from (realize you may have to go through a lot of steps because all slaves were not brought straight from Africa to the state where they ended up living--sometimes they went to the Carribean, etc. before coming to the United States, were traded all over the place.) It's work but it can be done. Eventually you can find the location where the ship picked up the people--from there you may be able to find out where the slaves came from originally (slaves were brought from all over Africa to ports where they were "processed."
Good luck! It should prove interesting!