The amplitude decay of folded longitudinal acoustic phonon oscillations in GaAs/AlAs superlattices grown in the [100] and [111] directions is studied as a function of carrier excitation density. Time-resolved pump-probe measurements in reflection reveal decay times on the order of several tens of picoseconds, which are independent of the excitation density for all phonons in the [100] sample and for phonons at wave vectors q≠0 in the [111] sample. In contrast, the decay time increases with carrier density for the phonon at q=0 in the [111] sample. This phonon couples to the photoexcited electron-hole plasma via the piezoelectric interaction. Friction in the carrier plasma induces a damping of the phonon oscillations. The impact of the piezoelectric phonon-electron coupling on the amplitude decay is reduced by screening at high carrier density, resulting in longer phonon decay times.