When were Blacks able to be baptized in the Mormon Church?

Yes. Black people could and did join the Church through baptism and confirmation. In 1835, one provision was added regarding slaves legally in servitude to masters. The provision was that enslaved people had to have the permission of their enslavers in order to be baptized. 

This provision came about because of the persecution that Mormons were receiving in Missouri, which was a slave state. Beginning in 1831, Mormons began moving to Missouri because Joseph Smith prophesied that this was the location of a second Zion (the first being Jerusalem). Missourians reacted violently to Mormons moving to the state. They feared that free Black Mormons would incite their slaves to rebellion. To try and temper the Missourians’ violent reactions to Mormons, missionaries in the South were instructed not to teach enslaved people without permission from their enslavers.