  We calculate the $\pi$, $\rho$, $\omega$, and $\gamma$ coupling constants
between the heavy meson doublets $(1^-,2^-)$ and (0^-,1^-)/(0^+,1^+) within the
framework of the light-cone QCD sum rule at the leading order of heavy quark
effective theory. Most of the sum rules are stable with the variations of the
Borel parameter and the continuum threshold. Then we calculate the strong and
electromagnetic decay widths of the $(1^-,2^-)$ D-wave heavy mesons. Their
total widths are around several tens of MeV, which is helpful in the future
experimental search.
