I've never heard of one. By the late antebellum it's just obvious to the white South that they can only grow cotton with slave labor. Black people are biologically suited to the climate in a way that whites are not, so that they actually thrive doing work that would kill a white man. (This isn't true, of course, but it's what they thought.) And even if they wanted to try white men, the poor white labor pool available for work on cotton fields was small and transitory. The stereotypical poor dirt farmer of the antebellum South more likely that not owns his own land. He might not make a lot of money on it, especially not hard cash, but subsistence level farming with a bit left over for a small cash crop is pretty normal.

Poorer whites may stick around, but opportunities for advancement in the established cotton states begin drying up. This is a problem in South Carolina within about twenty years of the cotton boom, leading to a steady stream of up-and-comers going west for new opportunities. Most of those opportunities were carved out of land that just recently had Native Americans removed from it, which tells you some of why Jackson was so popular in the South. The other main path for upward mobility involved finding work as a non-farming professional, for which there could be limited demand and which needed a fair bit of upfront work to get established. If you have the connections and means to get into that job, you're probably not the kind of person who would be in a hypothetical white plantation laborer pool anyway. A person of limited means could best hope to be hired on as an overseer supervising enslaved labor.

That leaves free blacks. Free blacks scare the crap out of the cotton states and they work hard to keep their numbers as low as possible. Even under draconian laws, they're understood as a direct challenge to the stability of slavery as a system. They cannot be allowed, outside of the sorts who might have proven connections to and alignment with the white elite. So their relatives born to enslaved women after acts we must consider well short of any usual notion of consent. If an enslaver frees and establishes enslaved children in some level of middling comfort, that's not a danger in quite the same way as those freedpeople remain singularly dependent on and adjacent to the white power structure in ways that a less privileged black person would not. It's not really something they're trilled with, but more livable for whites. As a result, African-Americans in some pockets of the Lower South (Mainly around New Orleans and Charleston.) form an anomalous class clearly somehow above slaves but of ambiguous relationship with poorer whites. Also not the plantation labor pool, though a few do well enough to operate plantations themselves.

The white labor pool is resistant to being used on plantations, like slaves would be, even if paid a wage. If you do that work, then you must somehow deserve it and be on a level with the slaves. That puts the lie to all the talk about the South as a classless society because it's a white supremacist society. The free black labor pool is small and largely unavailable. The Native Americans have been largely removed in the hope that they will quietly die or be violently killed by white people somewhere down the line. That doesn't leave a lot of room for free labor plantations.

But that doesn't mean free labor never grew cotton; it probably did on a small scale. Calling these operations plantations is stretching the term beyond any usefulness, but those yeomen from earlier could grow cotton just like big plantation operations. Maybe they could only deliver a bale or two, but doing so was a good way to get some of that elusive hard money or some kind of credit. (The credit is more likely, but you never know. The antebellum South ran on IOUs.) That bale or two might be grown from seed to harvest by free labor of the head of household and some combination of wife, children, and relatives.

But there's another but too: cotton cultivation is limited to the black belts until Reconstruction levels up the South's infrastructure a bit more. So the yeoman working his smallish plot to grow cotton does so in the plantation region of his state. He's part of a local network of favors and customary patronage centered on the local Big Houses, which often provide services like bundling small lots of cotton with their main harvest (for a better price), extending credit, and loaning (usually for one-off things like helping raise a barn) or renting out slaves. So our yeoman with a cotton sideline probably has at least limited access to enslaved labor if he wants it, and he almost surely does. Renting slaves can be a step toward buying your own. For the first few, some kind of mixed labor would go on with the yeoman and his slaves working together. If success came, more slaves progressively meant less white labor in the fields until eventually you might have just one guy ordering around teams of enslaved labor led by enslaved drivers (literal slave drivers) and we're back to the familiar plantation.