What has been the most frequent method of changing governments in most latin american countries?

Coup d etats (American intervention)

Explanation:

The most famous cases perhaps are the American intervention to destroy goverments with different interest as Salvador Allende in Chile. The military assitance is either provided direclty as troops and weapons or as information. With the Cold war , the US involment in changing regimes in Latin America became very widespread practice. And in most of the cases the countries suffered from a political, social and economical unstability.

Under a series of military rulers after the coup, Guatemala , Brazil , Argentina and most of the countries have turned into dictatorships.

The elites in the Latin American countries tend also to colaborate as corruption and favoring the establish order favors their relationships in the global capitalist markets.