Soviet-Paraguayan War of 1937-1992. IOTL Russian White emigres were pretty heavily involved in Paraguayan military as advisers and COs, capitalizing on their rich experience in semi-guerilla warfare across wast sparsely populated land (aka Russian Civil War). However, they didn't try to influence the country's politics. ITTL Russians, riding the wave of popularity after the war, get themselves involved in politics with Estigarribia. When Stalin's "Great Terror" starts, Estigarribia (under the influence of his White allies) declares a war on USSR to show his contempt for Soviet brutality.
Since both countries can't strike at each other (too far), the war remains a diplomatic curiosity for much of next 40 years. However, it becomes a sort of valuable asset after Somoza's ruling regime of Nicaragua loses to Sandinistas. Since Sandinistas rely on the USSR and Paraguay is, technically, still at war with Soviets, Paraguya becomes a front end for the CIA's "dirty war". Monies, equipment and "volunteers" are channeled through Paraguy to Contras.
Again, not much is different ITTL comparing with OTL for next 15 years. However, things become interesting again when Soviet Unions disintegrates and Yeltsin's Russia becomes a successor state. Yeltsin is desperate to shed his communist past, so he orders Kozyrev to sign peace agreement ASAP at ANY cost. Paraguyans couldn't quite believe their luck, but, being Latino guys full of bravado, they offer a condition that Russia should compensate all Paraguay's expenses incurred to wage this war, plus applicable interest. Kozyrev agrees. Peace is signed and rammed by Yetsin down the Duma's throats. Russia finds itself under legal obligation to pay billions of dollars (CIA expenses incurring to support Contras, plus interests). 1990s witness a wave of seizures of Russian property abroad, initiated by lawyers working for Paraguayan government.