This is really well covered in Albert Raboteau's "Slave Religion: The 'Invisible Institution' in the Antebellum South," if you want a very in-depth answer. It's actually more answers, plural, because there were many religions represented amongst enslaved people, including Islam, and the kinds of Christianity they adopted varied from region to region. But generally, enslaved people brought many elements of their African religions to Christianity when they did convert, though it took a long time for that to happen en masse. This made the transition easier, and is seen throughout enslaved people's religious life -- the use of broken pottery on graves, for example, is linked to Yoruban ideas about the ocean being where souls live after death, and the importance of Moses rests on both his position as a liberator of slaves as well as being drawn from the water, echoing that theme of water as a place of spiritual birth and rebirth. For enslaved people in Louisiana, the elements of West African religion were hidden behind various saints who became stand-ins for loa, or spirits, that were known to them in Africa. This is where Vodou derives its use of Catholic iconography for the loa.

I know I keep saying generally, but because slavery in North America was a two-hundred-year process spread out over half a continent by the time it was abolished in 1865, there are thousands of specifics. Trends are inherently general, and leave out a lot of those specifics. There's some enslaved people who converted to Christianity because they heard the argument that Africans were barbarian pagans, and they believed that conversion would make them more likely to be freed. (It didn't, sadly.) Some masters forced Christianity on their enslaved workers, believing that it was necessary to enforce discipline by making them accept a teaching that included the Bible verse, "slaves, obey your masters." However, other masters didn't want to convert their enslaved workers -- some, because sharing the same faith would make enslaved people their equals before Christ; some, because they had so many enslaved workers that it didn't matter what their religion was, especially on large plantations with high death rates; and some, because they believed that reading the Bible was a core requirement of Christianity and they did not want enslaved people to be able to read, fearing that reading would lead to rebellion, as it often did. Various clerics had different ideas about converting enslaved people. Some were all for it, and helped free Black converts, especially ones that were inclined to become preachers so that those Black preachers could reach enslaved people more effectively than whites could. Some hoped that enslaved people and their owners all being Christian would encourage masters to behave with Christian charity and kindness towards their enslaved workers, though they were often disappointed. Denomination also mattered -- Baptists were, in the 18th century, often imprisoned by colonial authorities for preaching their beliefs and because they would not only baptise but ordain enslaved people. George Liele was the first Black Baptist preacher, and he preached in slave quarters on plantations around Charleston, SC until he went to the British army for freedom during the American Revolution. He went on to Jamaica and started the first Black Baptist Church there, with a congregation of 400, enslaved and free, and a school attached as well. Masters in South Carolina and Jamaica were ambivalent about Liele. On the one hand, as noted above, there was a potential for Christianity to make enslaved people more docile and easier to control. On the other, the idea that enslaved people were people who needed saving and might desire to learn was an anathema to the slave system, and Liele was frequently forced off of plantations, arrested, and otherwise impeded in his evangelism.

However, by the 1820s and 30s, many enslaved people had been born in North America instead of brought from Africa. The connection to Africa dwindled with every generation born in slavery -- and some states like Virginia made breeding slaves their business instead of farming tobacco. It's around the end of the Early Republic period that we see most enslaved people having embraced some form of Christianity and the establishment of Black churches, especially in areas with a large free Black population. (New Orleans remained an exception, as most free people of color were staunchly Catholic, or so they maintained, even if they were also practicing Vodou.) Due to events like Gabriel's Rebellion, Nat Turner's Rebellion, and other early 19th century slave revolts, the teaching of literacy was forbidden to enslaved people. This meant that enslaved people were rarely their own pastors or ministers. Masters on larger plantations brought in ministers to preach a docile Christianity officially to their enslaved workers on Sunday. Masters with only a few enslaved workers often brought them with the family to church, though they were made to sit in the back, or in a balcony, or otherwise separated from whites. Enslaved people had their own churches that they created and maintained, especially on large plantations, and they met at night, in secret. They relied on revelation and on Bible passages memorised from the white preachers that came to their plantations, and they created the spirituals that we know today. This covert Christianity had a lot in common with West African worship -- the structure of spirituals is similar to Yoruban and Igbo songs, the use of bodies stomping, clapping, and slapping as drum beats echoes the importance of drumming in West Africa, and the call and response structure is another important West African commonality. Yet enslaved people understood this not as a syncretism, but as their own Christianity, one that drew on the evangelical traditions of the Methodist and Baptist preachers that had come to them in the 18th century. The emphasis was on ecstatic experience, the emotional drama of the conversion narrative, and the emergence of a new person with the acceptance of Christ. These are ritual structures shared between West African religion and Christianity, but the enslaved people really saw it as a Christianity that spoke to them rather than sneaking in Africanisms. The writings of free Black preachers of the period really speak to that, especially the conversion narrative of Jarena Lee within the Black Methodist Church.

Basically, and generally, it took two or three generations of being born in North America and the stop of the trans-Atlantic slave trade for Christianity to take complete hold in enslaved people in America. Without an influx of Africans with African language and African traditions to refresh the pool in America, Christianity more easily took root as a spiritual salve to deal with the humiliations and tortures of slavery. But because of the conditions and the people in which it took root -- enslaved, othered, tortured, and retaining a cultural memory different from the whites that planted Black churches -- enslaved and free Black Christianity emerged as a different religious worldview, with a strong emphasis on community, conversion, and justice. Black Catholics don't make up a large percentage of the American Church, but they too pushed for social justice when they came into parishes as participants instead of just showing up on baptismal rolls. I think the ability to take the master's tool -- Christianity -- and make it into something of their own to challenge white supremacy and slavery at the same time was a great appeal. And Christianity, as a missionary faith, has always been very adaptable to whatever circumstances in which it finds itself. So the answer is complex and convoluted, but generally relies on the end of the African slave trade, the evangelisation of Black converts, and the willingness of masters to enforce Christianity on their enslaved workers -- as well as enslaved people being able to subvert the masters' purposes in doing so within the Biblical text and Christian message itself.

Some other books to consider:

Eric C Lincoln, "The Black Church in the African-American Experience."

Albert J Raboteau, "Canaan Land: A Religious History of African Americans."

Paul Harvey, "Through the Storm, Through the Night: The History of African-American Christianity."

Jason R Young, "Rituals of Resistance: African Atlantic Religion in the Kongo and the Lowcountry South in the Era of Slavery."

Charles F Irons, "The Origins of Proslavery Christianity: White and Black Evangelicals in Colonial and Antebellum Virginia."

Emerson B Powery, "The Genesis of Liberation: Biblical Interpretation in the Antebellum Narratives of the Enslaved."

Katharine Gerbner, "Christian Slavery: Conversion and Race in the Protestant Atlantic World."