The first thing to be aware of is that for most of slavery's history, the planter class was very much resistant to the idea of Christianisation. Although we do have evidence that some planters saw converting slaves as a useful method of social control in the late eighteenth century, they were very much the exception to the rule; it's only really from 1830 onwards that we begin to see a meaningful effort to introduce Christianity to slave populations.
The extent to which that effort was successful has been quite seriously debated. We do know that a significant section of the slave community was converted to Christianity by the time of the civil war; at least one in ten slaves by that time were formal members of a church, and it has traditionally been assumed that a significant number of slaves were practising or semi-practising Christians outside of formal churches. This is probably a reasonable assumption to make; just like today, not every Christian - even every practising Christian - would be a Church goer, and not every Church goer would necessarily have to be considered a Church member.
The thrust of the conversion effort was not, however, made by plantation owners themselves - it depended upon the efforts of missionaries and clergymen in the region. There were probably not nearly enough preachers to sustain a meaningful, mass conversion effort on the plantations; particularly when many slaves lived on large, hard-to-reach rural estates where missionaries would not be able to stay long. Church instruction could not make up for this lack of manpower - there were nowhere near enough spaces in the south's churches to accommodate the bulk of the slave population, especially in localities where planters owned dozens or hundreds of slaves each.
The contradictions between the realities of slavery and the philosophy of the Christian religion were not lost on those exposed to white religion, either. Much like southern planters had to construct a warped concept of freedom, so too did they have to construct a Christianity that not only sanctioned slavery, but the systems of repression and violence needed to maintain it. There is certainly evidence of slaves rejecting the faith outright, and of others expressing that they were essentially 'going through the motions' to please their owners, often because they recognised either the hypocrisy of the whites - preaching the love and forgiveness of God whilst keeping and treating slaves so brutally - or were frustrated at the lack of a place for their kind in white churches.
It is also questionable just how Christian the faith embraced by some slaves was. Whilst certainly a significant minority were practising members of established churches, many more practiced their faith in private - either on or near plantations, usually in the form of secret gatherings for worship. These gatherings would often include practices and ideas with distinctly African origins, even if they were performed and expressed in a Christian context. This kind of practice was certainly not the kind of conversion the white planter class had hoped for, but it was certainly widespread. Many of the religious practices - both daily and secret - of slaves that have been taken as evidence for widespread, earnest Christian conversion betray clearly African roots upon closer inspection. Significantly, we see these practices even on plantations where owners enthusiastically embraced the cause of slave conversion - which would seem to imply some measure of overlap between those slave church goers and 'dissident practitioners' on plantations.
By the late period, there was widespread recognition that the Christianisation effort had not been an unbridled success: by 1850, every southern state had found cause to pass legislation restricting the religious practices of slaves, motivated by fear that rather than just being a means of social control or advancing southern white culture, religion could also be an inspiration for disobedience or revolt.
The picture by slavery's abolition is really quite mixed. Certainly a substantial minority of slaves became very sincere, earnestly practising Christians, with many attending Church; many more embraced alternative or syncretic Christian practice outside of formal institutions. But it is really quite unclear how universal this embrace of Christianity was and, more to the point, how legitimate it was: it is plausible that many of those who were ostensibly to converted were not really practising Christianity at all but a continuation of their traditional spiritual practices, dressed up as Christian worship. Others may have mixed traditional practice with Christianity so much so that the result may not be truly considered Christian worship, and such practices certainly were not the intended outcome of slave conversion efforts.
It seems reasonable to assume that the efforts of the southern planters were successful in that they exposed slaves to Christianity in a more meaningful way and on a larger scale than ever before, created a class of very devout enslaved Christians, and transformed wider slave religious practice. They were ultimately probably a failure as a means of constructing another system of social control, and it seems that a great many slaves embraced Christianity in name only or not at all.
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I also wonder how genuine these "conversions" were and if the slaves were just acquiescing so they wouldn't be harmed?