As a first step to the active manipulation of adsorbates by external, time-dependent electromagnetic fields, the infrared-laser driven selective excitation of molecular vibrations of adsorbates at metal surfaces is investigated here in the framework of time-dependent open-system density matrix theory. Special emphasis is given to the inclusion of vibrational damping, caused by the coupling of the adsorbate vibrations to possibly electronic substrate degrees of freedom. For the example system NH3/Cu, a non-Markovian, two-mode open-system Liouville-von Neumann model for the vibrational relaxation of an excited adsorbate is proposed. After studying the field-free decay of excited adsorbates, it is shown that even in rapidly relaxing environments optimal IR laser pulses in the picosecond domain can be designed which lead to temporarily high populations of selected target states of adsorbates at metal surfaces.