Costa Rica -> Costaricense

Canada -> Canadiense

Estados Unidos -> Estadounidense

Etc

Forgive me if I fail to answer your whole question since it is well beyond my area of expertise; however, I thought I would try to illuminate the question about the Provincias Unidas de Sudamérica. I spent quite a bit of time searching primary sources for the terms you presented but to no avail. I was looking in documents that included the primary independence thinkers and government officials of the early national period in the Río de la Plata including Belgrano, Moreno, Alberdi, Rosas, and others. They also include records from newspapers, cabildos, and congresos nacionales from this period. After searching for a while, I concluded that individuals in the Río de la Plata did not refer to themselves in the political literature in the first fifty years of independence, at least in the sixty or so primary sources I have access to, as provinciasunidense or sudamericano.

Well that’s weird! In political literature specifically devoted to national identity, why did no one refer to a collective identity? How did they talk about a “we” collectively? To answer this, I am going to depart from my AskHistorian friends. Many people are giving answers that assume that there was an identity that needed a word to describe that identity. In reality, there was no unified identity to describe. Although it was called Provincias Unidas, at no point during those ten years were they anywhere close to united. In fact, anything resembling a true nation with defined cultural, ethnic, and social identities really did not exist until well after 1870. So Provincias Unidas is a complete misnomer; it did not exist in the peoples’ minds.

In reality, they were still debating the very name of their new political entity fifteen years after independence. In 1825, Diego E. Zavaleta, José Francisco Acosta, Julián Segundo Agüero, Valentín Gómez, Juan José Paso, and others in the constitutional congress were still debating what they should call this space. Was it Provincias Unidas de Sudamérica? Or was it Provincias Unidas del Río de la Plata en Sud América? Or was it Provincias Unidas del Sud de América? Or was it simply Provincias Unidas del Río de la Plata. They struggled with nomenclature because, since Napoleon’s invasion and subsequent severing of ties, sovereignty, according to traditional Spanish law, reverted back to “el pueblo.” In both Spain and the colonies, “el pueblo” was assumed to mean localities. Given the fragmentation of the Río de la Plata, the vast empty spaces that existed there, and the tiny popluation, the people of the Río de la Plata experienced this reversion at a local level. They looked to nearby urban areas for guidance...not to a nation as a whole. Buenos Aires tried to assert itself as the representative of the NATION, but this quickly fell apart into civil war.

So what then did these early independence thinkers call themselves? José Chiaramonte, a preeminent scholar on national identity in the Río de la Plata region prior to and during the independence period, explains that the terms people used were relative and vague, changing when encountered in a particular context:

...en la rioplatense por ejemplo, podemos observar que se era español frente al resto del mundo, español americano frente a lo español peninsular, rioplatense frente a los peruano, provinciano frente a lo capitalino, porteño frente a lo cordobés...La dominación española no dejó otra cosas que un mosaico de sentimientos de identidades...cuya relación con los sentimientos de identidad política construidos luego de la Independencia será variada y pocas veces armónica. (Chiaramonte, Ciudades, Provincias, Estados: Orígenes de La Nación Argentina (1800-1846). Buenos Aires: Emecé Editores, 1997, p. 62).

Most commonly, as I’m searching through primary sources, I see the region described as theoretically as “la Patria,” which is the vague term for the fatherland...the specifics of this term were undefined. Clear affiliation with a nation simply did not exist. As you might expect, in terms of political discussions, they refer to “el pueblo” frequently to which they identify clearly. Contemporary foreign travelers like the Robertson brothers from England, did not refer to an “argentino” or “sudamericano.” Instead, they describe individuals at a local level from their particular provinces, preferring terms like “correntino” or “paraguayano.”

Vagueness was common because there was no affiliation among people with a larger group. For example, the article EL CONFEDERACIONISMO PORTEÑO DE 1816 published in La GAZETA, a Buenos Aires newspaper discusses the disunion in the supposedly United Provinces:

La federación que de poco tiempo a esta parte ha entrado en las cabezas de muchos de nuestros patriotas, desgraciadamente excede de los límites de una federación que deje en unión a todos estos pueblos. La exaltación y calor de sus ideas, los celos que se demuestran de unas a otras provincias, las rivalidades, las desconfianzas, los odios, y la envidia, todo demuestra que los federalistas de la América del Sud no se ceñirían a establecer un solo gobierno federal, sino que querrían desprender cada una de las provincias de las otras. Aquí tenemos los mismos escollos que temer que en la América del Norte. La Banda Oriental lindando con los portugueses; las provincias del Perú con las de Lima; Mendoza con los enemigos de Chile; y Buenos Aires expuesto a las invasiones de ultramar.

In this excerpt, there is no “us” to which the people can identify. Since there was no national identity, there was no need for a pronoun that could collectively identify such a diverse group of people as one entity. Following independence, identities remained scattered at a local level.