It did happen. Cases are less well documented though. And I have no doubt it was far less common. If a woman was pregnant from a slave the family would often cover up the pregnancy and sell the child into slavery. Just as children of white men and black women were slaves. Rape was often alleged as well. Women were expected to be chaste and just accusing a man's wife or daughter of having relations with a slave was a huge allegation and offensive to the entire family. So, it isn't as though people went around making such claims idly.

Charles Ball was a slave who wrote a well known autobiography in 1837 and in it he describes a planter's daughter who had an affair with a slave and got pregnant. The child was taken from her and she was essentially shunned form society.

Captain Richard J. Hinton, who was an abolitionist, claimed every black man he had ever truly befriended claimed a white women had coerced him into sex at some point (I am sure you can find the quote if you google it). I don't think he is a source to be taken on his word (it is anecdote, hearsay, and he had an agenda, one we agree with, but still an agenda). But I do think it gives some suggestion that at least such things were talked about. And even if they weren't being recorded for history there was at least some acknowledgement that these things could occur.

Also, abortion was around and used in the 19th century. Obviously, it was unsafe and since it was unregulated we don't have numbers. But there were ways to avoid having a pregnancy detected. And if you are a white woman in the South in the 19th century the prospect of giving birth to a mixed race child (and the shunning that would arise from that) would probably make it worth the risk.

Also, in 1892, Ida B. Wells published a series of famous pamphlets about lynching laws. Part of it went into cases where black men were accused of rape but it was later found that it was consensual (mostly if a woman confessed since it wasn't as though they were given fair trials). Wells actually cites the incidents she is referring to. She doesn't just rely on anecdote. She has a famous quote I will butcher about some white women just preferring black men (this was in 1892). That is after slavery but a lot of the dynamics were still in place. And we are talking about some people who had lived through slavery (Wells, herself, was born a slave in 1862).

I'm sorry I don't have more but it wasn't a phenomenon people liked to discuss. But we do get echos of such occurrences through sources like the ones I mentioned and others.

I know of cases in Colonial Maryland where white women bore children to African or African-American slaves. They were all servants, mostly indentured servants which was the legal slavery for white folk in colonial America. While I am sure it was not common, it does not appear to be exactly uncommon either. I did not see any records of slave owners indulging in this behavior, but my reading is not exhaustive.

In most cases, they were found out because they bore "mulatto" children. The women were fined, which would be paid by their masters if they were not free (and their indenture period was lengthened to repay it) - and if they were free and could not pay, would result in their indenture until it was repaid, and were generally whipped somewhere around 20 lashes. Their children were almost universally bound into slavery until at least age 21 or more often age 31. The male slaves were whipped - around 40 lashes, and their masters had to also pay a fine. Source: Free African Americans of Virginia, North Carolina, South Carolina, Maryland and Delaware by Paul Heinegg (you can read it for free at http://www.freeafricanamericans.com)

Some examples:

Eleanor Atkins appeared before the court in 1697/8 and was 20 years old. She received 24 lashes.

Elizabeth Day was an indentured servant who in 1710 (at age 15!) and again in 1713 confessed to the Charles County court to bearing mixed-race children; the first at least was to a slave named Quasey belonging to her master. I do not see what her sentences were.

One of Elizabeth Day's descendants, Mary, born around 1744, confessed to the Prince George's County court in 1764 that she had a "Mulatto" child. Mary was ordered sold for seven years and her five-week-old daughter Lydia was ordered to be sold to her master, Henry Purdie, until age 31.

Mary Phillips, born around 1714, servant of William Lock, was convicted by the Anne Arundel County court in June 1734 of having an illegitimate child "begott by a Negro." The court bound her six-month-old daughter to her master until the age of thirty-one, and in March 1735/6 the executor of Lock's estate brought her into court to be sold for the last seven years of her sentence. [Judgment Record 1734-6, 4, 410].

Mary Pickett, born say 1703, was the servant of Edward Offutt on 27 August 1723 when she confessed in Prince George's County court that she had a "Malatto" child. The court sold her and her child to William Offutt [Court Record 1723-6, 77, 139].

Mary Plowman, born around 1685, was an indentured servant in Kent County, Delaware - she had a child by a black slave named Frank in 1704. She was sentenced to 21 lashes and additional time in servitude to repay her master for the court fees, and Frank received 39 lashes.

Elizabeth Price, an indentured servant born around 1685, was convicted in 1703 of fornicating with a black slave belonging to her master, and was sentenced to 21 lashes and an additional 18 months servitude - and her child was bound as a slave to her master until age 21.