This paper is focused on the study of acoustic metasurface cloaking, based on the use of appropriate ultrathin pseudosurfaces that may act as cloaking devices for a finite range of frequencies. The technique consists in tailoring the appropriate acoustic surface impedance which cancels the scattered field of a diffracting spherical obstacle placed in the trajectory of an impinging acoustical wave. Our numerical simulations of both near and far fields show a significant reduction of scattering cross section for a moderately broad range of frequencies, confirming the effectiveness of surface cloaks (easier to manufacture and less cumbersome than their bulk counterpart). We also go one step further by proposing a realistic structure obtained by quasiperiodically patterning the surface of a spherical layer. The effective properties of the metasurface are obtained in the framework of homogenization theory and confirm this realistic route to surface cloaking for acoustic waves.