A somewhat general answer:

Tl/dr: the general mainstream approach of the Southern church(es) to the abuse of slaves - including slave rape - was opposition, in that they taught an idealized vision of the Christian master/slave relationship. In this theoretical system, slavery was ordained by God for the benefit of all, and there existed an interlocking set of mutual duties; slaves to obey their masters, and masters to both care for their slaves, and not to abuse them unjustly (aka, "reasonable" punishment for disobedience/etc was fully accepted), and perhaps most importantly, masters were to facilitate the slaves becoming good Christians.

For a longer answer, it's first important to note that "the church" in America has always been extremely fragmented and diverse; at some point in American history you can find "a church" that teaches nearly any doctrine you can possibly imagine. Southern churches in the antebellum period were similarly diverse. The major denominations included the Baptists, Methodists, Presbyterians, and Episcopalians, all national denominations, and the first three of which split into Northern and Southern denominations over the question of slavery, and which therefore featured most prominently in the religious discussion over slavery within the South. Even within these denominations there could be significant differences - Southern Baptists in particular are still famously more of a loose confederation of churches with similar principles than any sort of centralized organization.

That said, American Society in the 1800's, to include (and perhaps particularly) Southern society, was very publicly religious and Christian. As the Northern abolition movement was powered to a great degree with those claiming that slavery was inherently unchristian, and as the abolition movement progressively drove many voices defending slavery out of leadership in many Northern churches, so Southern defenses of slavery shifted from primarily claiming that it was clearly permissible (around the time that the Constitution was drafted), to declarations that the Bible didn't just permit but required the existence of slavery in a Christian society, particularly the slavery of Africans.

As part of this, a number of noted theologians arose in the South who sought to comprehensively address and defend slavery from a Christian perspective. Please note that by no means am I claiming that most individual churches or pastors did so, or that those who did so spent significant amounts of time preaching against slave abuses, though likely some did (and likely suffered in popularity as a result). In general, these theologians, and at times their conferences, crafted a system wherein scripture and the will of God divided humanity and fit different people and groups for different roles in society, one of which was that of slaves. This system both defended the social divisions among whites in the Southern aristocracy, and permanently relegated blacks to the status of slaves. However, it also recognized blacks as persons, and just as aristocrats and poor whites owed certain Christian and social duties to each other, so masters and slaves did as well. Slaves owed obedience; masters owed a certain duty of care, body and soul. The South Carolina Methodist conference, for example, declared that masters sinned against their slaves by “excessive labor, extreme punishment, withholding necessary food and clothing, neglect in sickness or old age, and the like.” A notable faction among Southern clergy preached against the laws that banned slaves from learning to read, on the grounds that they needed to be able to read scripture; however, this position failed to make any headway amongst those who held political power in South, as they viewed it (probably correctly) as an essential part of keeping the slaves repressed. At least one notable southern pro-slavery theologian - whose name I will edit in when I get home and have access to my books (edit - see below) - was, by the start of the civil war, beginning to think that the general failure of masters to adhere to their Christian duties to their slaves was undermining the theological justifications for church support of slavery. Such warnings, however do not seem to have been making much headway in the popular consciousness, and during the lead-up to the war Southern churches were far more likely to spend time thunderously promoting the part of these theologians' doctrine that permitted and required slavery within society, and attacking the Northerners for attempting to undermine God's order, than they were to risk undermining it themselves by highlighting the failures of owners to behave as good Christians towards their slaves. That said, some of them did speak up during and after the war to basically say "I told you so" and lay the blame for Southern defeat(s) on the fact that slaveowners had failed to discharge their Christian duties to their slaves, and thus removed the blessing of God from their society which would have otherwise ensured their victory.

I'll edit in the sources from my library when I get home, but the article linked above touches on much of what I've discussed: https://opinionator.blogs.nytimes.com/2012/04/27/the-south-the-war-and-christian-slavery/

This source has some notes on the Church splits: https://christianhistoryinstitute.org/magazine/article/broken-churches-broken-nation

Edit: in addition to my general knowledge, many of the details informing the above come from William Freehling's "The reintegration of American history," and particularly the chapter on James Henley Thornwell, the theologian whose name escaped me above.

Freehling's thesis, which seems to comport with everything else I've read on Southern social organization, is that Antebellum southern society was fundamentally based in paternalism, which applied to family structure, to the social structure of whites, and to the institution of slavery. This method of social organization - with its interlocking set of mutual duties - had numerous philosophical and theological defenders in the South. Thornwell was a Presbyterian minister who Freehling refers to as "the Antebellum South's greatest theological abstractionist" based on his rigorous, honest, and deep philosophical examination of potential social organizations and ensuing advocacy for the institution of slavery, among other issues. For example, Thornwell framed the social roots of the conflict between North and South as a social structure wherein wherein superiors were required to care for inferiors (the south) vs a hierarchical society where the powerful were responsible for nothing except their own selfish advancement (the industrial, capitalist north). Yet these theological abstractionists, Freehling notes, were generally defending slavery based on an idealized framework of what righteous, paternal slaveholding should entail, rather than the reality of how slaves were actually being treated by their masters.

Thornwell in the 1840's advocated for laws that would place some restrictions on the absolute power that slaveholders held over slaves; specifically, he wished the states to ban the break up of slave families, as tearing apart marriages was unchristian, and he wished to prevent slaveholders from hindering efforts to convert slaves to Christianity. This effort failed miserably in spite of the fact that they were essential parts of the theological defense of slavery; slave owners were much less interested in theological details than in maintaining their absolute authority. Thornwell died in 1862, and in his last years he was deeply troubled by the failure of southern slavery to meet the standards which he believed it must in order to be defensible for a Christian. He apparently reached the point of speculating - though not in public - that some form of gradual emancipation might be necessary if southern slavery could not be brought up to Christian standards, which was a shockingly radical sentiment for a southerner at the time, and something that would likely have landed him in serious trouble socially and professionally had he stated it in public.

I hope that someone else can offer more specific info; I find it hard to believe that some pastor somewhere did not write a letter or a sermon condemning slave rape. But at the same time, it cannot be emphasized enough the extent to which in Southern society, a master/landowner/patriarch was, for the most part, accountable to no one except God, not even to a minister and only to the state in the most extreme of circumstances; what happened within the bounds of his household could generally be expected to stay within those bounds, and any public comment on the resemblance of the children of slave women to a white master might well be cause for a duel or a lawsuit, or "merely" sworn enmity, in that honor-focused society.

Hello - as this post is somewhat unusual in its framing the mod team does want to clarify that yes, the source here is not original (as acknowledged in the linked site, it's a replica). The use of 'church' in any singular sense also doesn't quite work in an American context. However, a) we don't require that questions are perfectly phrased or framed (we'd be a pretty terrible educational resource if we did!) and b) the underlying question of 'how did organised religious groups respond to sexual violence against enslaved people?' is an entirely legitimate and worthwhile question to ask. We ask that only people able to provide an in-depth answer to the question comment below - otherwise it is not necessary to comment on the basis of the question.