As a result of strict regulations of phthalate plasticizers, alternative non-phthalate forms are desired and increasingly used. This work presents a synthetic method for alternative plasticizers (dialkyl succinates and adipates) via esterification of succinic and adipic acid with alcohols: butan-1-ol and 2-ethylhexan-1-ol. Ionic liquids were synthesized by the reaction of triethylamine with over-equimolar (1:2.7) amounts of sulfuric(VI) acid, which were used as an acidic catalyst and solvent. The two-phase liquid–liquid system was formed during the reaction due to immiscibility of the esters with the ionic liquid. This phenomenon is a driving force of this process, shifting the equilibrium toward the product formation. As a result, dialkyl succinates and adipates were obtained in high yields (99%) and selectivities (>99%), under mild reaction conditions at 70–80 °C and using a 4:1 molar ratio of alcohol to acid and 15 mol% of catalyst. The catalyst was recycled 10 times without any loss of activity. This alternative method is highly competitive: it involves a simple procedure for product isolation as well as a high yield and purity of the resulting esters. These advantages make this method sustainable and promising for industrial applications.