Butterflies, butterflies everywhere.
How would Artigas and the Federalist crew there be mollified?
With a Federal Constitution. IMHO, that's the only way to prevent the decades long civil war.
I tend to agree with Thanksforallthefish. The issue is how to avoid a war with Portugal/Brazil, or to win it in the face of the superior Portuguese fleet. While a Portuguese invasion in the 1810s might be avoided, it will happen eventually: Brazil will want access to the Parana and Uruguay rivers so they can access Matto Grosso. I guess there are two ways to ensure a (somewhat) lasting peace with Brazil. One is to defeat them on land. If, somehow, a land offensive becomes doable despite the Brazilian naval blockade (which doesn't affect military action in land, but asphyxiates the economy) and the offensive begins to liberate slaves as it advances, the Brazilians might be brought to the negotiation table under fear of a slave revolt. The other is what happened in OTL. A weaker side in the civil war negotiates with Brazil military assistance (in the form of troops) in exchange for free navigation of the Parana and Uruguay rivers.
At this point, butterflies are swelling. The Montevideo business elite will become a counterweight to the Buenos Aires business elite, and this will dramatically alter the political and military situation. Instead of a single province the sea access of the entire country, we have two. Furthermore, if butterflies mean Rivadavia isn't in power by the time Sucre moves to liberate Bolivia (likely, as the Uruguayans will not want Rivadavia in power), then whoever is in charge (if anyone) can make a bid of keeping Bolivia as part of the United Provinces or whatever the country is called in ATL, further changing the political composition.
We also have different leaders. Artigas isn't going into exile. Lavalle's coup might not happen, either because there is no war with Brazil, because unitarians are in power when the war happens or Lavalle is out for whatever reason (the war happens when Lavalle is fighting the Spanish, he gets killed in battle, whatever). So while there might be a Unitarian take over at some point, it might not include the assassination of Federalist leaders. Even more, troops from Uruguay and the Liga Federal available, Rosas might not rise to power and could remain just a rich land owner until the day he dies.
If Dorrego is still exiled and finds his way into the USA he might be the hinge that makes Federalism (and Artigas) palatable to Buenos Aires. With political and military support, he could be elected as president, under a federal constitution, and cut short the civil war.
San Martin could return, as long as there is relative peace when he does. Given his age, I see him training a cadre of good military officers before going into retirement and dedicating the rest of his years to wine making or something. Unless he wants to get into politics, but given how linked internal politics and war were at that time, I don't see it.
Whatever butterflies you choose, the situation will still be very unstable. There will military takeovers in the provinces from time to time. IMO, Unitarians will be relative weaker than in OTL, but civil war is still in the cards. A lasting peace with Brazil isn't easy. Argentina will be subject to gunboat diplomacy, although with (if) a more united internal front, the consequences would be less damaging. Paraguay is in a tricky position. On one hand, without an independent Uruguay the War of the Triple Alliance is butterflied away. On the other, is effectively land locked and can be potentially blockaded by Argentina.
If butterflies cause a shorter or less bloody civil war in Argentina, Paraguay can find itself facing aggressive Argentine politics aimed at annexing the country. In such a situation, I could see Paraguay joining Brazil in a war against Argentina once/if the situation in Argentina stabilizes, if such a war happens.
If they reach the late 19th Century as an independent country, they will be a lot better than in OTL. They won't have the losses of the War of the Triple Alliance and, through the 20th Century, they can not only become a customs/smuggling paradise for the Argentine and Brazilian middle/upper class, they can also take over OTL Uruguay's role as a fiscal paradise, all of which will boost their economy.
As for Argentina, butterflies. Pick the one you want. The civil war and the power dynamics inside the country will be completely changed.