It would be exceptionally difficult to put an exact number or rate on acts of self-destruction of enslaved people in America or the Americas. In the case of Antebellum United States, the idea of enslaved Africans committing suicide was largely purposefully ignored or dismissed. Enslaved suicide ran counter to the narrative that Southern planters prided themselves on (or at least used to push back against Northern Abolitionism), that is the idea of paternalism. Enslavers in the South often argued that they treated their enslaved workers well enough that the idea of suicide would not even cross their minds. Why would it, they would argue since we take care of our 'workers'?^(1) Denying suicide also preserved a level of social/religious standing for Southern enslavers, lest they would be viewed as exceptionally cruel by their counterparts. An additional layer of racism was present in this time period as well. It was argued among some Southerners and Northerns alike that enslaved Africans were too "cowardly" to commit acts of self-destruction and citing the lack of suicides as evidence for their claims.^(2)
These claims, of course, are not factual. While the exact records can be hard to come by, given the circumstances surrounding the actions in the Antebellum South, there are records from the Middle Passage. The process of enslavement in chattel slavery meant that humans were regarded strictly as cargo to be bought or sold, so the loss of life was recorded for both insurance and record sake. Historian Terri Snyder writes, "...one study of surgeons' logs for the period 1792-1796 reveals that 7.2 percent of captive Africans killed themselves at some point during capture, embarkation, or along the Middle Passage."^(3) Sommerville also details an "epidemic of suicide" in Cuba that resulted in a royal commission to investigate the spike (a spike that resulted in almost 20% of enslaved peoples taking their own lives).^(4)
I am not sure if it is possible to accurately calculate the rate at which enslaved African's committed suicide in the Antebellum South. Once these enslaved peoples were sold in the US, they were under the legal ownership of private buyers. How those individuals chose to keep or not keep records, destroy records, or lie was up to them. One can look at records from other parts of the Americas, however, for more evidence towards rates of slavery and these will also change depending on what areas are looked at (Caribbean, South America, Brazil, etc). I have not stumbled across any hard numbers over an extended period of time, though, except for numbers during certain/specific periods (like the case of surging suicides in the Cuban example). Suicide, however, was perceived differently be Europeans and enslavers than it was by Africans.
Take the infamous Igbo Landing in 1803 in which a mass suicide of enslaved Africans occurred. This could be attributed to the idea of transmigration in which death would result in their souls being transported back to a happier place in Africa. These ideas carried themselves all the way to the 1930s during the federally funded Writers Project where an individual interviewed recalls stories he was told as a child about death resulting in the ability too "fly up in the air and all fly off and gone back to Africa." Such ideas had ties in religious beliefs held by some enslaved Africans. That is not to be a monolithic statement, however, as many individuals held different and complex beliefs or could have viewed the act of self-destruction as a way to escape the unimaginable brutalities of enslavement. Either way, this final act of resistance that many people chose is an expanding area of academia and there are tons more that could be said/expanded upon.
Other sources not directly cited but that I've referenced/read in the past:What is Slavery? By Brenda E. StevensonFatal Differences: Suicide, Race, and Forced Labor in the Americas By Marc A. Hertzmanlink (free to read): https://academic.oup.com/ahr/article/122/2/317/3096204
Recreating Africa: Culture, Kinship, and Religion in the African-Portuguese World, 1441-1770 By James Sweet