Well, in theory you could launch a telescope to some orbit and a starshade to the orbit obtained by reflection in the plane that passes through the central body perpendicularly to the direction to the object you want to observe:
Then, assuming perfectly Keplerian orbits, if you synchronize the telescope and the starshade to move perfectly symmetrically, then the line which passes through them will always point to the observed object. (Of course, if they move perfectly symmetrically, then they will collide in the points where their orbits inntersect, so there's that.) Part of the time, the telescope will be in front of the starshade, though, but you can make this fraction small by making orbits highly elliptical.
These two orbits don't have to lie in the same plane, they just have to be symmetric to each other w.r.t. the plane perpendicular to the direction to the star. If you make the orbits non-coplanar, then the central body won't block the view when the telescope and the starshade are in apogee.
I doubt that this would work in practice, though. Influences of other celestial bodies and irregularities in the gravity of the central body would affect the orbits, and the direction of the line connecting the telescope and the starshade will change. But I don't know how quickly.
As far as I can tell, this is the only solution under the assumption of perfectly Keplerian orbits. If the direction of the line that passes through two orbiting objects stays constant over some period of time, then the components of their accelerations perpendicular to that direction must be the same. This is possible only if they are at the same distance from the central body, i.e., they are symmetric to each other w.r.t. to the plane passing through the central body and perpendicular to the line connecting the two objects.