The formation of a planetary system from the protoplanetary disk leads to destruction of the latter; however, a debris disk can remain in the form of asteroids and cometary material. The motion of planets can cause the formation of coorbital structures from the debris disk matter. Previous calculations have shown that such a ring-like structure is more stable if there is a binary star in the center of the system, as opposed to a single star. To analyze the properties of the coorbital structure, we have calculated a grid of models of binary star systems with a circumbinary planet moving in a planetesimal disk. The calculations are performed considering circular orbits of the stars and the planet; the mass and position of the planet, as well as the mass ratio of the stars, are varied. The analysis of the models shows that the width of the coorbital ring and its stability significantly depend on the initial parameters of the problem. Additionally, the empirical dependences of the width of the coorbital structure on the parameters of the system have been obtained, and the parameters of the models with the most stable coorbital structures have been determined. The results of the present study can be used for the search of planets around binary stars with debris disks.