Totally by accident I've just happened to run across the 2014 open access paper A peculiar stable region around Pluto with the abstract below.
The purpose of the paper was to see if stuff might already be in some long-lived orbits around the system, things that New Horizons might pass near and photograph, or perhaps even collide with.
I don't know if New Horizons looked or not, but if you wanted to put something there in the system that would remain stable for a while, this three-body orbit will last quite a while. To that end I've just asked Did New Horizons look for "sailboats" in the Pluto-Charon system's sailboat region? Did it pass through it or avoid it?
Giuliatti Winter et al. found several stable regions for a sample of test particles located between the orbits of Pluto and Charon. One peculiar stable region in the space of the initial orbital elements is located at a = (0.5d, 0.7d) and e = (0.2, 0.9), where a and e are the initial semimajor axis and eccentricity of the particles, respectively, and d is the Pluto–Charon distance. This peculiar region (hereafter called the sailboat region) is associated with a family of periodic orbits derived from the planar, circular, restricted three-body problem (Pluto–Charon–particle). In this work, we study the origin of this stable region by analysing the evolution of such family of periodic orbits. We show that they are not in resonances with Charon. The period of the periodic orbit varies along the family, decreasing with the increase of the Jacobi constant. We also explore the extent of the sailboat region by adopting different initial values of the orbital inclination (I) and argument of the pericentre (ω) of the particles. The sailboat region is present for I = [0°, 90°] and for two intervals of ω, ω = [−10°, 10°] and (160°, 200°). A crude estimative of the size of the hypothetical bodies located at the sailboat region can be derived by computing the tidal damping in their eccentricities. If we neglect the orbital evolution of Pluto and Charon, the time-scale for circularization of their orbits is longer than the age of the Solar system for bodies smaller than 500 m in radius.
[...]The relevance of the sailboat region for the New Horizons spacecraft is addressed in Giuliatti Winter et al. (2014). In this work, we verified that the nominal trajectory of the New Horizons passes near the region of the sailboat region trajectories and we also identified the location of the densest regions, which corresponds to the highest probable location of particles of the sailboat region.
The set of periodic orbits, in the synodic frame, for different values of CJ presented in Fig. 2. The barycentre is located at 0, the origin of the coordinate system. The large and small black dots indicate the location of Pluto and Charon, respectively.
Figure 7. A sample of periodic (in black) and quasi-periodic (in yellow) orbits, in the synodic frame, for (a) CJ = 2.786 and 2.936, (b) CJ = 3.016 and 3.056, and (c) CJ = 3.116 and 3.224. Pluto is represented at the position (−0.1, 0) and Charon at (0.8, 0). The quasi-periodic orbits presented here are those with the largest amplitude of oscillation which correspond to the largest islands in the Poincaré surface of section (Fig. 2).