In The Half Has Never Been Told, the author describes owners giving slaves alcohol as a strategic decision. When slaves were driven in coffles (groups of slaves chained together for perhaps hundreds of miles for transportation), they were given alcohol to dull their pain and make them less resistant to the killer pace they had to keep, and to dull their hunger. They were also often given alcohol at slave auctions so that they would be numb to the horrors of being sold away from their family and friends, and less able to resist.

In Frederick Douglass's autobiography, he devotes a few pages to the issue of why slave owners liked to get slaves drunk, and what slaveowners did to encourage it. In his area ( Maryland), slaves had holiday between Xmas and New Year, and they were expected to get drunk at that time. Slave owners held contests to see who could drink the most. Slave owners took offense at the slaves who decided to use these days off to work for themselves to better their conditions, as an implicit criticism of the slave owner, as well as a suspicious tendency to think for themselves. Also, slave owners worried that all those days without work might sow the seeds of insurrection, so keeping them drunk discouraged that, and also make slaves feel so sick at the end of it that it would seem to them that freedom wasn't all that great. And slave owners would say that, see, they weren't fit to take care of themselves, so they belong enslaved, for their own welfare.

In both sources (one focusing on Maryland, the other on Louisiana, Mississippi, and other Deep South cotton areas), whiskey is the main drink mentioned, so perhaps beer was a rarer commodity at the time.

In the United States a slave's access to alcohol was restricted under a state's slave codes which typically forbid people other than the slave's masters from providing alcohol to enslaved people. Frederick Douglass wrote in his autobiography that masters often encouraged their slaves to drink whiskey to excess during holidays as a means to both let off steam from the year's hard work and as a way to disillusion slaves with the notion of freedom by convincing them that freedom would entail drunkenness and all of the woes that accompanied it.^1 He also mentioned in a speech at a temperance rally in Scotland that masters gave their slaves alcohol in order to discourage them from plotting their escapes.

As for whether or not slaves would have had access to beer, by the early nineteenth century the majority of the United States preferred drinking cider or watered down spirits. Brewing required a greater amount of capital and skilled labor than cider pressing and tended to be restricted to urban areas or places with a sizable German population.^2 Distilling whiskey was even more common because it served as a means for farmers and plantation owners to make use of their surplus corn. Many plantations had their own cider presses and distilleries, but Belle Grove in Virginia (originally owned by a family of German immigrants) is the only one I know of which possessed a brewery. So to answer your question yes, it is entirely possible that an American slave in the nineteenth century would never have had a beer.

1. Frederick Douglass, Narrative of the Life of Frederick Douglass, an American Slave, pages. 74-77.

2. W.J. Rorabaugh, The Alcoholic Republic: An American Tradition, pages 107-111.