We report the detection of large-amplitude, quasi-harmonic density fluctuations with associated magnetic field oscillations in the region surrounding the diamagnetic cavity of comet 67P. Typical frequencies are ~0.1 Hz, corresponding to ~10 times the water and ≲0.5 times the proton gyro-frequencies, respectively. Magnetic field oscillations are not always clearly observed in association with these density fluctuations, but when they are, they consistently have wave vectors perpendicular to the background magnetic field, with the principal axis of polarization close to field-aligned and with a ~90° phase shift w.r.t. the density fluctuations. The fluctuations are observed in association with asymmetric plasma density and magnetic field enhancements previously found in the region surrounding the diamagnetic cavity, occurring predominantly on their descending slopes. This is a new type of waves not previously observed at comets. They are likely Ion Bernstein waves, and we propose that they are excited by unstable ring, ring-beam or spherical shell distributions of cometary ions just outside the cavity boundary. These waves may play an important role in redistributing energy between different particle populations and reshape the plasma environment of the comet.