Most Southerners who advocated ending slavery favored either manumission or colonization and the majority of these people were to be found in Virginia. George Mason, for example, has long been considered an early advocate of ending the institution, and by the end of his life so was Washington.
The Southern movement was not as radical nor vocal as that which started to pop up in the North in the early 19th century, and no Southern anti-slavery movement matched the zeal of Garrison or Beecher, et. al. Southern anti-slavery proponents were not militant and after Nat Turner most refrained from advancing the message if they still harbored any support for eradicating slavery.
Peter Kolchin’s American Slavery is a solid treatment of the institution, as is Louis Filler’s Slavery in the United States of America.