I haven't heard the term coherent JT effect yet. However, cooperative JT refers to situations where JT distortions in one unit cell (or structural unit) of the lattice cause a distortion in neighbouring unit cells. A good example is the JT effect in perovskite manganites such as LaMnO3. In the latter, each Mn ion is surrounded by six O ions located at the corners of an octahedron. A distortion of one octahedron causes distortions of neighbouring octahedra leading, for example, to the so-called CE phase.
I have not come across this term many times.But I found it in few papers,where they discuss distortion in LaCoO3 and rule out coherent Jahn teller effect.Here I am posting one link,where you can find the use of the similar term.
http://arxiv.org/abs/1208.2304
I am not clear about the distinction between the two.
Reading the article it seems they use coherent as a synonym of cooperative. Actually they use the word cooperative once in the article to account for multiple stabilization efects of e-type distortions working together. So I guess there is no such difference.
The only possible distinction is when the Jahn-Teller distorted polyhedra are disordered therefore a regular pattern of M-O bond distances is observed over an average crystalline structure although for each M locally the M-O bond distances are still different. No example comes to the top of my head right now but I hope you get the idea.
Here is a review paper on this:
Reports on Progress in Physics Volume 38 Number 1 G A Gehring and K A Gehring 1975 Rep. Prog. Phys. 38 1 doi:10.1088/0034-4885/38/1/001
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