We present the results of a computational study of ZnO in the presence of Co and Mn substitutional impurities. The goal of our work is to identify potential ferromagnetic ground states within the (Zn,Co)O or (Zn,Mn)O material systems that are also good candidates for piezoelectricity. We find that, in contrast to previous results, robust ferromagnetism is not obtained by substitution of Co or Mn on the Zn site, unless additional carriers (holes) are also incorporated. We propose a practical scheme for achieving such p-type doping in ZnO.