  Resonant locking of two planets is an expected outcome of convergent disc
migration. The planets subsequently migrate together as a resonant pair. In the
context of circumbinary planets, the disc is truncated internally by the
binary. If there were only a single planet, then this inner disc edge would
provide a natural parking location. However, for two planets migrating together
in resonance there will be a tension between the inner planet stopping at the
disc edge, and the outer planet continuing to be torqued inwards. In this paper
we study this effect, showing that the outcome is a function of the
planet-planet mass ratio. Smaller outer planets tend to be parked in a stable
exterior 2:1 or 3:2 resonance with the inner planet, which itself remains near
the disc edge. Equal or larger mass outer planets tend to push the inner planet
past the disc edge and too close to the binary, causing it to be ejected or
sometimes flipped to an exterior orbit. Our simulations show that this process
may explain an observed dearth of small (< 3 Earth radii) circumbinary planets,
since small planets are frequently ejected or left on long-period orbits, for
which transit detection is less likely. This may also be an efficient mechanism
for producing free-floating planets and interstellar interlopers like
`Oumuamua.
