I suspect having slightly elliptical orbits wouldn't make too much of a difference either, but I haven't checked. Click on images to start them moving, or to stop them. Dragging changes viewpoint. It helps your CPU if you only have one running at a time. First, for reference, this is what a typical trajectory through a binary star system looks like.
Stable orbits are few and far between.
The star system is circular, with one star 4x the weight of the other. The stars will have gone around once, the planet will have gone around twice, and they should all be in the same position every time. It's a strobe effect. The planet has been given nonnegligible mass and slight errors in the starting position, so it should wander a bit. See, it's stable.