Cigarettes made up about 5% of the market until the 1910s. Even less before the invention of the cigarette machine in the 1880s. You'll need a colossal nerf on tobacco itself--a novel disease or whatever--to prevent the settlement of the South. The majority of the market was pipe tobacco, chewing tobacco, and cigars. It still is in parts of the South, such as that much of Tennessee/Kentucky's tobacco is not used for cigarettes compared to, say North Carolina's tobacco.
But I don't know if you can prevent cigarettes from being invented. It's just paper and tobacco, very simple in construction. You'd need to kill tobacco itself. From what I've read, there seems to be plenty of ways of suppressing the cigarette industry, keeping it to maybe 15-20% of the tobacco market and thus not making it ubiquitous as it became OTL. The best way of getting rid of cigarettes might be the Prohibitionist movement, which targetted cigarettes as well as alcohol, and after alcohol was banned, some of them triumphantly proclaimed "cigarettes are next!" Over a dozen states banned cigarettes in the late 1910s/early 1920s, and many others restricted their sale. But the movement was basically spent the moment it began. General Pershing proclaimed that cigarettes were needed for the American Army in WWI, and it could not have helped the cause of the anti-tobacco movement that some of the same people who wanted cigarettes banned were later on in France passing out cigarettes to American soldiers. Which of course, happened to get a ton of people hooked and thus expanded the market and made the companies even stronger.
But if cigarettes are that small of the market,
everything is affected. Starting with no ashtrays in cars--a common feature from the late 20s onward. Also including advertising--the tobacco industry was at the cutting edge of advertising. Granted, the same advertising geniuses who helped build Big Tobacco worked for many industries, but they'll be either losing a huge client or somehow failing with that client. That's hard to imagine, since what these advertising executives were doing was basic psychology which is pretty guaranteed to work on a vulnerable population. The cigarette industry basically created a market for tobacco. The guy who created the "Tobacco Trust", J.B. Duke (who also basically made the cigarette industry as it was and as it is even now), found it hard to imagine that cigarettes would ever be much bigger than they were in the late 1910s, and he was utterly, utterly wrong. You'd be proving him right.
Nerfing cigarettes is strengthening the early anti-tobacco movement (which targetted not just cigarettes, since they were such a small part of the market), nerfing the strength of advertisement firms in the 20th century, and keeping public perception anti-tobacco. The anti-tobacco movement failed in part because they felt too "Victorian" in morality and not "modern". And the sad part is, Big Tobacco was able to capture the feminist movement and portray women smoking as a symbol of liberation (which they
still were doing into the 1970s with female-targetted cigarettes). How can you beat that? Probably by finding a way to keep men smoking, unless you also want to kill the early feminist movement which gained a lot of strength based on women's suffrage. Now, one of the main reasons a lot of people didn't smoke was because of the effects on health. If you were into athletics and such, many people realised that smoking was no good for you even after a few cigarettes. That might be a way to keep the Army from demanding cigarettes. I couldn't imagine what other drug you might want to hand out. I'd hope more caffeine, but amphetamines are a prospective as well.
Overall, you'd get a healthier public, but also more prevelance of other forms of tobacco. Now, I mainly focused on the American tobacco market, but I can't imagine without a strong American market, that tobacco would take off as much globally. You'll see a lot of people worldwide surviving a few years (at least) longer, and public spending on health being spent elsewhere. Asia especially--cigarette use is huge in China and Japan, and with the nerf to the tobacco industry, they might not be able to hook nearly as many people. For China especially, that could have huge repercussions. But there's still the issue of other forms of tobacco, but I think a lot of that is fairly limited in terms of success, thus capping the strength of Big Tobacco. E-cigs might be invented earlier, though, since a concern over cancer links (which will be found by the 50s/60s) and a desire to create a new market might help them become prominent far earlier. Maybe as a sort of "space age" way to get your hit of nicotine, in a way that unlike tobacco, is "completely safe", which with science as it was in the 50s/60s, Big Tobacco will actually be able to say and promote as such.
Those were just examples. But something would likely replace Tobacco.
England's first efforts at colonizing were in the American south. Those first colonies would try something to become viable. King James, who hated tobacco, I think tried to encourage silk worms.
King James didn't have much influence on tobacco's popularity in either England or elsewhere.
But for crops, the South is pretty limited. Various grains grow best, but that's not exactly a cash crop. Yaupon (
Ilex vomitoria) could be popularised, though. Lots of people claim the association of yaupon tea with black drink, the American Indian ritual drink that caused vomiting, prevented the popularity, but yaupon was still extensively consumed by whites throughout the colonial period and into the early 20th century regardless. Maybe it could find the right audience in Europe and take off like coffee or tea did.
Other than that, rice, indigo, etc. are the best options pre-cotton gin, and they can't grow everywhere. So the end result is much more small-scale yeoman farmers in North Carolina, Virginia, Kentucky, Tennessee, etc. That's a huge effect on slavery. Also, yaupon is not domesticated, and judging by its relative yerba mate, domestication could take centuries, so plantation-style agriculture cannot work for yaupon. Other potentials are tea and coffee, which OTL were small-scale in the South. As far as I know, all these crops can only grow in the Deep South, since the Upper South has too cold of winters/shorter growing seasons than the coastal/Deep South.