Ambient sun drying is the method most used by Indigenous communities for preserving fruits and seeds harvested from the forest. It is an effective method to increase the shelf-life of highly perishable foods and prevent spoilage until important bioactive compounds can be extracted at distant locations. The ambient sun drying kinetics and oil extraction of the pulp and seeds of commercially important oleaginous fruit directly obtained from the rainforests and swamps of Guyana, namely Astrocaryum vulgare (Awara), Astrocaryum aculeatum (Kuru), Oenocarpus bacaba (Turu), Mauritia flexuosa (Ite), Euterpe oleracea (Acai), Caryocar nuciferum (Souari), Attalea maripa (Kukrit), and Carapa guianensis (Crabwood), were studied. The fruits were dried under ambient conditions from initial moisture contents ranging from 24–71% to a final moisture content of 5%. Three models, the Lewis model, the modified Page model, and the standard logistic function (SLF) model, were utilized to model the drying kinetics and to estimate the parameters governing the drying process. These models were demonstrated to fit the experimental data with excellent goodness of fit (>0.98). The SLF, never used before to model drying kinetics, was observed to be the best-suited model overall, with the highest correlation coefficient and the least Chi-square (χ2). Depending on the fruit type, the estimated point where the maximum drying rate occurs varies from 35 min to 350 min for sun-dried fruit pulp and up to 4000 min for sun-dried kernels. The steepness of the drying curves varied from −0.5 to −3.5 g/min. The results of this work will aid in the design, development, optimization, and control of the ambient drying processes of economically and functionally important oleaginous forest fruits. This knowledge will assist in addressing the key challenge of spoilage faced by Indigenous communities in the preservation of tropical oleaginous fruits and seeds, possibly aiding in the preservation of functional characteristics of the extracted oils and adducing to the sustainable economic utilization of such fruit.