Energy levels and radiative rates (A-values) for transitions in Cr-like Cu~VI and Zn~VII are reported. These data are determined in the quasi-relativistic approach (QR), by employing a very large {\em configuration interaction} (CI) expansion which is highly important for these ions. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST and other available theoretical data, for a majority of the levels. The A-values (and resultant lifetimes) are listed for all significantly contributing E1, E2 and M1 radiative transitions among the energetically lowest 322 levels of each ion. ; Comment: 7p of Text and 6 Tables will appear in ADNDT (2016)