Industrial-scale rare earth extraction is typically performed by liquid-liquid extraction with large amounts of solvents, acids and organophosphorus ligands. An alternative is to use these extractants in supercritical CO$_2$ (SC-CO$_2$), where the crucial operating parameter is their solubility. Different molecules with amidophosphonate backbones have been synthesized and investigated in view of improving their solubility in SC-CO$_2$ and thereby their cerium extraction capacity. The CO$_2$-philicity of these extractants was adjusted by attaching branched or linear alkyl chains with four, six and eight carbons. Using a dynamic gravimetric setup, the solubility and cerium extraction capacity of these molecules were measured to vary from 1.56 to 2.47 mmol$_{ligand}$.mol$_{CO2}$$^{-1}$ and 0.25 to 0.46 mmol$_{Ce}$.mol$_{ligand}$$^{-1}$, respectively.The two properties were correlated and in both cases the highest values were obtained with a diisobutylamine chain. Solubility measurements between 313 and 331 K and between 13 and 28 MPa shows that optimal condition is (320 K ; 28 MPa).