Wait, wait, no later or no earlier than 1816? Because no later, I don't really see much changing in the colonization. Maybe if, somehow, an important sedentary Indian civilization develops and it's sort of integrated into an European empire. But, as a colony, there isn't much economic activity to be developed by the 18th century, even if the colonizers aren't Spaniards. And of course, it wouldn't even be an Argentina, but a completely different country whose borders just might be similar to OTL Argentina.
Now, if you meant no earlier than 1816, then we might be up to something. The schism between Buenos Aires and the Liga Oriental (and Artigas) has already started, but Uruguay might not be lost in the long run. If it remains as part of the United Provinces, it will work as a counter weight to Buenos Aires, although it would create far more troubles with Portugal/Brazil. It might end up being more trouble than it's worth.
The key is to convince enough porteños (people from Buenos Aires, for those who don't know) that unitarism won't be accepted. That's unlikely. Barring that, avoid the Portuguese invasion of Uruguay and have Buenos Aires defeated and 'conquered' in battle by the Liga Oriental. If a federal constitution can be issued, roughly accepted and the civil wars avoided or greatly diminished, we may be up to something.
After 1816, the Independence War will be fought outside current Argentine borders. There is the chance, if there is a national (preferably, a federal) government to keep Bolivia by staging an offensive into the Alto Peru by the time San Martin and Bolivar close into Peru. While that provides quite a mineral wealth, it doesn't necessarily add in the long run - check Bolivia's history for that. Resource extraction a great power does not make. Economic activities which help develop a middle class do.
Now, if we do avoid the civil war, there is the chance of the gauchos slowly turning into a rural middle class, which will help the slow development of an internal market and might prevent politics from turning too fraudulent and paternalistic. But, at that point, we are already entering wank territory: everything goes right, nothing goes wrong.
In any case, a more peaceful Argentina during the 19th century will mean earlier immigration and education. It will still turn into a agrarian-based export economy once the 2nd Industrial Revolution hits and local craftsmen will go broke, unable to compete with British and French industrial goods. But, by the turn of the century, it will be more populated, better educated, and will have a growing middle class. In OTL, by that time Argentina was one of the first countries to experiment with aircraft, movies, setting bases in Antarctica and slowly begun to develop a nascent industry. Think of that on steroids.
During the course of the 20th century, the hard differences have to relay in either keeping the British Empire going or getting China or India to become powerful much, much earlier. Avoiding the Second Sino-Japanese war and, if possible, the whole WWII would help. That will cause the agrarian sector to keep its importance as the main world powers would be net importers of food, instead of net exporters, as the USA. The green revolution will hit and boost the productivity of the sector. Light industries should develop if the major powers get involved in war with each other and can't provide the Argentine upper and middle classes with consumer goods. If the USA keeps out of such a war, the better.
We should also tackle social conflict in a wankish way that's not violent, nor corporatist. With a bigger middle class and earlier education, resulting in an overall better educated populace, I think things might be too hot earlier than the 1940s. The key is to force a compromise which, as I've noted, would be wankish. Maybe some something like the New Deal has to be put underway when an ATL '29 crisis hit, so the economy gets boosted and social conflicts softens at the same time.
Then comes the challenge of avoiding economic mismanagement (not hard if East Asia is buying grain) and keep the military from interfering with politics. The OTL 1930 coup it's not hard to avoid. Political parties (initially the UCR and later the conservatives) reaching the military when they note they can't reach power by other means has to be avoided. This could be avoided if there is a not so fraudulent election system in place during the late 19th century (so no UCR as we know it) and if the conservatives (if they are a force to taken into account in ATL) find a way to remain a palatable alternative to the electorate. All this might be related to whatever means were reached to dilute social conflict. It would certainly help if the officer corps doesn't see as itself as part of a not really existing aristocracy. Again, we are entering wank territory here.
If there is no WWII, Argentina could take advantage of the window of opportunity between the first spoken movies and the invention of proper dubbing and subtitling to push her cinema to the Spanish speaking markets. And, with it, advertise whatever industrial exports can be manufactured in the country. Remaining an important player when Hollywood comes back in the earnest would be a challenge, and one that would be faced by all major movie producing countries. Maybe a powerful China, with its massive internal market, can act as a counter-weight Hollywood?
In any case, by the end of this wankish route, you have a highly educated, economically sound country, with an important cultural presence abroad, ATL Argentina.
I haven't touched military might. Such a wankish ATL Argentina could afford powerful, at least for the region, armed forces. The issue about it is which are the ATL threats. Does ATL Argentina require to project power well beyond her coasts, so a strong navy with one or two carriers are required? Is she part of a worldwide alliance and her commitments with the alliance require powerful and modern armed forces? Is there a regional threat instead? Or is the region fully pacified, the neighboring countries are allied of each other and the armed forces are sort of guarding a 'Fortress South America' from potential major powers from outside the continent?
Ditto for nuclear weapons. I think they are within our current technical capabilities, so a wanked ATL Argentina would be able to have them, if there is the political will to do so. The thing is, is there the need IITL to have them?
