Tropical South America is one of the world's largest natural methane (CH₄) emitting regions, yet regional methane budgets remain highly uncertain due to poorly constrained wetland emissions and sparse atmospheric observations. Here, we quantify methane emissions from the Amazon, Orinoco, and Paraná river basins for 2010–2019 using the Jena CarboScope atmospheric inverse modelling system. We investigate the variability in the methane budget through a series of sensitivity experiments. Our inversion estimates methane emissions of 4.44 ± 0.88 Tg CH₄ yr^-1 for the Orinoco, 28.60 ± 5.15 Tg CH₄ yr^-1 for the Amazon, and 30.10 ± 3.95 Tg CH₄ yr^-1 for the Paraná basin, together accounting for ~59 % of the total estimated South American methane emissions (105.5 ± 11.10 Tg CH₄ yr^-1). The inversion substantially modifies the seasonality and interannual variability of prior wetland emissions in all three basins. The dominant source of posterior variability differs among basins. The data-sparse Orinoco is most sensitive to the wetland prior, indicating strong dependence on prior information. Regional observations mainly constrain the Amazon, which accounts for 55 % of the variability in South American posterior methane emissions. The Paraná is largely insensitive to regional observations and is constrained primarily by the global network. These results show that uncertainty sources vary across South America. Improving wetland priors and expanding regional atmospheric measurements are essential for reducing uncertainty in regional methane budgets.