I was surprised that I couldn't find any simple-looking solutions in this atlas. At first I was looking for Lagrange orbits, but maybe it makes sense to exclude them if zero-mass bodies aren't allowed. I think the equilateral triangle ought to be included though.

They’re not stable except at L4 and L5, and they all assume oke body to be massless. Arguably they are 2-body orbits for that reason. Not sure but suspect that this atlas contains non-massless bodies.