The wikipedia article describes P-type and S-type orbits for planets in binary star systems. There are possibly some other quasistable funky orbits.
But what about a central planet? I have added one to the diagram with its "W-type" nonorbit. The Ptolemy planet is parked between its two suns of equal mass. It does not orbit but sits there in the middle, centered between the stars. Physics wise it seems like it should be stable. How the planet would get there is a different matter - probably it would need to be a construct or perhaps a survivor of a more complex multiplanet arrangement in which other players are now gone and Ptolemy is sitting still.
Of course the stars would need to be suitably far away from each other such that their combined light did not bake a planet that we want to be redolent with sweet alien life. Ptolemy would be outside the habitability zone of either star considered alone, and probably there is no P or S type orbit around these wide spaced binaries that would not bake or deep freeze the planet.
The joint efforts of the 2 stars produce this small habitability zone centered between.