US Surinam
There are alot of limitations on how such a state could realistically have happened. Latino-majority states are unlikely because of American racism. We have no non-Anglo-majority states, despite having had the populous Puerto Rico, Cuba and Philippines in our hands. The problem is that Latinos were strictly second class, treated like kids, and run by politically connected Americans mostly for their bank accounts. Poverty and health both stayed quasi-medieval in Puerto Rico until they were allowed to choose ALL their leaders. So, a simply conquered state, especially as big as Chile or Peru would stay in rebellion and probably be let go.
Plus, we had no real Pacific Fleet yet, making Chile, Peru, and Bolivia hard targets; and it would've been a long haul back then. And, there's alot of land, alot of it decidedly hard to dominate easily. It's one thing to beat an army or two, it's quite another to occupy and hold that kind of thing. Sorry, Rushchurch.
BUT, I'm not seeing anything impossible in Anglo-settled South America. And, neighboring Guyana's improbably because virtually all's jungle, and too many Anglos would've died in this time before they figureded out quinine.
POD: $2/3M added to Louisiana Purchase, in exchange for Surinam. Surinam was Dutch at the time, but since the Dutch Republic at the time was a Napoleonic puppet state, I think that would've looked more like opportunity to the French negotiating the deal. The Frenchman doing the deal sold it by pointiong out, very rightly, that it was much faster and easier to travel to Surinam than most of the North American turf transferred in the deal, and by pointing out the successful Dutch peanut plantation.
The American Government incorporated Surinam as a territorial government, with slavery. Population was light, so the Jefferson Administration and first Surinam administration decided to encourage Anglo population with the target of making it eventually an Anglo-majority state. They made land available cheap to American citizens who immigrated. Aggressive lawyers ended up with the valuable already-developed plantations, of course, as happened to so much Mexican turf Texas. And nobody ever asked any questions about where slaves came from, unless they were lily-white.
At that, only the northern part would see much Anglo population, because southern Surinam's mostly rainforest - see above, before quinine. Anglo population became a majority by the late 1840s, not that non-Anglos were ever well-counted in the territory.
The territory got more military protection than most because of its isolated statusl, and because it made a handy base. There's still an AFB there. There were revolts and slave raids, of course, just as in OTL, but population was never so heavy. After a decade or so, settlers were informally told they could expect no protection in the rainforested South; even if rainforest was cleared, rebels and slave bands kept out of sight in the nearby still uncleared part. Troops reached Surinam in 1865 - 2 years later than OTL - to enforce the end of slavery there. But, sharecropping and Jim Crow replaced the outright slavery like in other ex-slaveholding states. Racist rule was finally replaced at the same timeframe as in other Jim Crow states, and with the same need for action to make it happen.
Surinam's development toward statehood was on the slow side because of its big non-Anglo cultures, its rainforest south, transit costs, and the differences in what crops worked well; Latinos and indios had long figured that out, but they didn't get so much attention, of course. Southerners had dreams of Surinam helping alot with the balance against the populous, high-immigration North, like the OTL Southern-Cuban dreams, but it didn't work out that way.
Surinam was admitted to the US in March of 1912, the same year as Arizona and New Mexico. Thanks to A/C and modern medicine, it's now a high-growth state like Arizona.