  We demonstrate rotational cooling of the silicon monoxide cation via optical
pumping by a spectrally filtered broadband laser. Compared with diatomic
hydrides, SiO\+ is more challenging to cool because of its smaller rotational
interval. However, the rotational level spacing and large dipole moment of
SiO\+ allows direct manipulation by microwaves, and the absence of hyperfine
structure in its dominant isotopologue greatly reduces demands for pure quantum
state preparation. These features make $^{28}$Si$^{16}$O\+ a good candidate for
future applications such as quantum information processing. Cooling to the
ground rotational state is achieved on a 100 ms time scale and attains a
population of 94(3)\%, with an equivalent temperature $T=0.53(6)$ K. We also
describe a novel spectral-filtering approach to cool into arbitrary rotational
states and use it to demonstrate a narrow rotational population distribution
($N\pm1$) around a selected state.
