I do sympathise with this issue - I was very worried when I realised that we needed a professional to talk to and there were none labelled "poly-friendly" in our area.
We got incredibly lucky - the lady we worked with did a lot of work for Catholic Charities, locally, so I didn't hold out much hope. She hadn't heard of polyamory but promised to do some research.
Once she had done that she asked me lots of questions to clarify and to try to explore whether this really was what I felt in my heart, and not an excuse to "cheat with permission". She started watching Big Love and laughed about some of the issues that they came up with.
Then we realised that she was very, very good - I could explain stuff to her that my mono partner just didn't understand and she found a way to explain it back to my mono partner in ways that utterly made sense to her, asking me for confirmation and guidance. It was an utterly positive experience. I have since recommended her to other poly folks who have told me that she has been great for them, too.
So I asked her why didn't did say that she was "poly friendly", and she said that that would (unfortunately) cause others to avoid her as an "alternative" therapist, which was a limited niche that she didn't want to dive into. I followed this up with the question about how poly folks should find a good poly therapist when they don't advertise, and she said that in her opinion, any Good therapist should be able to do the research and put themselves in the patient's shoes without judging or looking for "solutions".
However, I have seen on threads here that others have had less than positive experiences.
I guess it's one of those things that you need to find someone you can trust to be open-minded, and that can often take some time.
A while back I bookmarked some articles (don't know how I found them) that are aimed at healthcare professionals working with polyamory patients - I printed some of them out and gave them to our therapist and she said that they were very useful, because they talked about issues from THEIR point of view. Here they are:
Good luck in your search!