The mechanisms for generation of long-lived spin coherence in a two-dimensional electron gas (2DEG) have been studied experimentally by means of a picosecond pump-probe Kerr rotation technique. CdTe/(Cd,Mg)Te quantum wells with a diluted 2DEG were investigated. The strong Coulomb interaction between electrons and holes, which results in large binding energies of neutral excitons and negatively charged excitons (trions), allows one to address selectively the exciton or trion states by resonant optical excitation. Different scenarios of spin coherence generation were analyzed theoretically, among them the direct trion photocreation, the formation of trions from photogenerated excitons and the electron-exciton exchange scattering. Good agreement between experiment and theory is found.