We study coherent phonon transport through organic, π-conjugated molecules. Using first principles calculations and Green's function methods, we find that the phonon transmission function in cross-conjugated molecules, like meta-connected benzene, exhibits destructive quantum interference features very analogous to those observed theoretically and experimentally for electron transport in similar molecules. The destructive interference features observed in four different cross-conjugated molecules significantly reduce the thermal conductance with respect to linear conjugated analogues. Such control of the thermal conductance by chemical modifications could be important for thermoelectric applications of molecular junctions.