It really depends on the time and place. Speaking very broadly (since I'm no expert on this, and I can really only talk about Paraguay in this scenario) chances for a Communist revolution begin to rise post-1959, because that's when you have an example of a Communist regime in Cuba actually working (or at least not falling apart/being successfully invaded by the United States.) It also acts as a base from where 'revolution' can spread; look at Che jetting off to Bolivia to instigate an insurgency there.
It is always a temptation to look at South/Latin America, see all the right-wing military dictatorships and conclude that Communist revolutions were a distinct possibility. That can be right in certain cases, and wrong in others. Certainly in Chile, you had a hard-left administration under Allende form, although that didn't need a revolution. In Peru, the regime of General Juan Velasco Alvarado bucked the trend of most military juntas on the continent by siding with the Soviet bloc, thoroughly frightening Washington. In Paraguay and Brazil too, you had various left-wing groups fighting against campaigns of repression by military governments. And there was the case of the Venezuelan Communist Party, which decided to try out an armed struggle against the relatively popular (not to mention legitimate) government of President Romulo Betancourt.
But the reasons (most of) these attempts failed were threefold. First, the lack of a popular base. In Paraguay, dissidence mainly found form through the speeches and actions of intellectuals unpopular outside of the cities. In Venezuela, Communist attempts to rally the peasantry into supporting an armed insurgency failed because they supported the reformism of President Betancourt.
Second, divisions were inherent in the Communist movements. In Ecuador, the Sino-Soviet ideological split severely hampered hard-left hopes as that nations Communist 'vanguard' fought amongst itself on similar lines. In Venezuela, the Cuban envoys sent to assess that nation's Communist Party's potential for an armed struggle condemned what they saw, and thus condemned any military aid for such a venture. In Paraguay, the Paraguayan Communist Party couldn't get a toehold in the anti-Stroesner opposition, and in 1967 split along the same lines as its Ecuadorian counterpart had. In Brazil, the leftist opposition didn't split just twice; twenty different groups purported to be the true voice of the Brazilian people.
Thirdly, the United States held an interest in keeping South America friendly, which precluded highly questionable actions by the Central Intelligence Agency and, if necessary, military intervention. In 1962, the dangers of letting that policy slip had made themselves very apparent when Fidel Castro invited the USSR to station missiles 90 miles from the coast of Florida. Even beforehand, CIA fears as to the susceptibility of Guatemala to Communist influence had led to Operation PBSUCCESS, id est the coup d'etat that had toppled President Arbenz. Then of course there's the Bay of Pigs example. As a more acceptable (and probably more effective) method of combating leftist radicalism in South America, Presidents Kennedy and Johnson had endorsed the 'Alliance for Progress,' an American effort to combat radicalism by investing heavily in lifting the South American lower classes out of poverty. Since that would take decades at best, the CIA did indulge in covert activity in the meantime, resulting in the creation of institutions like The School of the Americas and helping dump left-wing dissidents into the Pacific.
But as Robert Dallek explains in his book 'Nixon and Kissinger,' there were also realists in the State Department who regarded CIA active operations in S. America with some scepticism. By 1970, circa the beginning of preparations for the overthrow of a (possible) Allende government, men like Winston Lord were calling for the cessation of any covert activity in Chile because it completely undercut US policy in other parts of the world. Another expert thought the idea that Chile could be another Cuba, i.e. a dangerous example to follow, was ludicrous, given an Allende government, occuring in a country with a history of democratic elections, would crumble under its own contradictions. Moreover, it would be difficult to imagine the USSR wishing to replicate the Cuban Missile Crisis yet again.
Based on my own limited knowledge then, I would consider the threat of a full-blown Marxist revolutions in South America as comparitively small. There's simply too much riding against it; the lack of a popular base, ideological division and American antipathy. 1) and 3) combined shut out large swathes of the continent from Soviet interference. Allende succeeded because he came to power democratically, in an economic enviroment (the Copper market, Chile's main export, wasnt doing well from '64-'70) partly conducive to his political message (his right-wing opponent still won 35% of the vote, compared to 36.2 for Allende.) Moreover, until the murder of General Schneider, the Army wasn't likely to intervene to stop his legal ascent to the Presidency.
For a more widespread Communist success in South America, intervention in the form of increased KGB support (hand in hand with an understanding of what is actually going on in S. America, on the part of the Centre), coupled with the lack of a Sino-Soviet split, would have to occur. You'd probably have to discredit CIA covert operations in a manner similar to the Church Committee, but a lot earlier, not to mention inculcating an attitude among policy analysts in the State Department that such intervention is not only morally unacceptable, but diplomatically unsound. And have that idea permeate to the highest sections of the Executive, which is what failed to happen under the Nixon Administration.