We report the results of an [O III] λ5007 spectroscopic survey for planetary nebulae (PNe) located within the star clusters of M31. By examining R ∼ 5000 spectra taken with the WIYN+Hydra spectrograph, we identify 3 PN candidates in a sample of 274 likely globular clusters, 2 candidates in objects which may be globular clusters, and 5 candidates in a set of 85 younger systems. The possible PNe are all faint, between ∼2.5 and ∼6.8 mag down the PN luminosity function, and, partly as a consequence of our selection criteria, have high excitation, with [O III] λ5007 to Hβ ratios ranging from 2 to ≳ 12. We discuss the individual candidates, their likelihood of cluster membership, and the possibility that they were formed via binary interactions within the clusters. Our data are consistent with the suggestion that PN formation within globular clusters correlates with binary encounter frequency, though, due to the small numbers and large uncertainties in the candidate list, this study does not provide sufficient evidence to confirm the hypothesis.