Ultracold bosons in a triangular lattice are a promising candidate for observing quantum spin liquid behavior. Here we investigate, for such system, the role of a harmonic trap giving rise to an inhomogeneous density. We construct a modified spin-wave theory for arbitrary filling and predict the breakdown of order for certain values of the lattice anisotropy. These regimes, identified with the spin liquid phases, are found to be quite robust upon changes in the filling factor. This result is backed by an exact diagonalization study on a small lattice.