A question came up while chatting with a friend — how do you tell the editors of the journal to not ask certain people for a review? Say you submit a paper to a journal and in the cover letter you want some language to the effect that “please don’t choose Dr. X as a reviewer, since they will be biased.” This must be a relatively common situation, especially where people have axes to grind, and what better way to grind them than while reviewing the other camp’s paper or grant proposal?
Let’s create a cartoon situation: suppose Dr. X really hates your guts (intellectually, of course) — this is actually the case, and not just your own misperceptions of Dr. X. I know that at some schools for tenure cases the candidate can give a list of people not to ask for letters. But in the context of paper submission, hows can you politely suggest that Dr. X may not be the most objective reviewer for your paper?
An Ergodic Walk 
I am not sure how to do it for papers, but you can do it for grants. NSF grants typically contain a list of suggested reviewers, and a list of “un-suggested” reviewers.
I would probably let things be, unless it is a very serious issue. If the latter, then maybe write to the editor, and say why?
Well, it can become a serious issue if Dr. X essentially shoots down every paper you write on topic Y. I am not sure how often that extreme scenario happens in practice — it seems Dr. X would have better things to do with their time…
ToN has lists of preferred/non-preferred reviewers. I never invite from either list.
Ah, a very Buddhist path. I think that some journals don’t have such a list though. Having lists makes the problem of phrasing moot.
When submitting a paper to Elsevier, you have are asked to include a list of recommendations and a list of antirecommendations for the referee. You have to justify each one of them.
As I mentioned above, I guess this is not standard in all fields. Do you think this is a good way to deal with the issue? It seems good because it addresses up-front the possibility of biased reviews (positive and negative). But for niche topics, it might limit the reviewing pool a bit too much.
It is not common in my field either. I was suprised to learn this was the case when I submitted to Advances. I remember my coauthor and I agonizing over it. There was somebody we wanted to include in the list of antirecommendations, but we chose not to do it in the end.