These are my Coticules. Most coticules will be two layer stones. The yellow-ish layer is the Coticule. The darker layer is some sort of slate. If it is naturally occurring slate (Coticule often occurs in nature mixed in with slate deposits) it will probably be a layer of Belgian Blue slate. Many Coticules these days are glued to a slate backing after being mined. This actually helps the Coticule, since they can be quite brittle when the slate layer is not present. In the above pictures, the one in the box is glued; the smaller one with the uneven layer of slate is naturally occurring. The smaller pieces are just slurry stones.
Some Coticules are known for the vein from which they were mined. The pictured one in the middle, I am told, is a Les Latneuses Coticule. I have no way to prove its provenance, but it has given me some really great edges.
@MilkCrate, I hope this gives you an idea of how to identify a Coticule.