Generation mechanisms of long-lived spin coherence of two-dimensional electron gas (2DEG) have been studied theoretically and experimentally, the latter by means of a picosecond pump-probe Kerr rotation technique. CdTe/(Cd,Mg)Te quantum wells with a diluted two-dimensional electron gas have been addressed. Strong Coulomb interaction between electrons and holes, which results in large binding energies of neutral and negatively charged excitons (trions), allows selective addressing of exciton and trion states with resonant optical excitation. Different scenarios of coherence generation have been analyzed, namely, direct trion photocreation, formation of trions from photogenerated excitons and electron-exciton exchange scattering.