It's easier if you know what kind of therapy (also called "modality") you want to use. For example, let's say you know you want EMDR, then you could just look at the EMDRIA directory. Same with Internal Family Systems and many other modalities. Many of them have their own directories.
Most online directories also let you filter by treatment approach/technique/modality. So once you know what you want, you can filter by that.
THEN, make sure you actually interview your potential therapist and tell them you don't want any CBT. It's crucial to interview/consult before committing to working together. The quality of your relationship with your therapist is seven times more important to your outcomes than the kind of approach they use. So it must be a good fit.
This list of therapy approaches is a good place to start learning - I know it seems overwhelming at first. My recommendation: Start by reading about Psychodynamic Therapy, Eye Movement Desensitization and Reprocessing Therapy (EMDR), Internal Family Systems (IFS), Narrative Therapy, and Somatic Therapy. All of those are nothing like CBT. There are many others, this is just a start.
Some therapist directories for you:
- Open Path Collective (affordable therapy, $40-$70)
- Psychology Today
- Therapy Den
- Mental Health Match
- Good Therapy
- Therapy Tribe
- ZenCare
- Therapist.com
- Inclusive Therapists
- Therapy for Queer POC
- Therapy for Black Girls
- Therapy for Black Men
- National Queer & Trans Therapists of Color Network
- Asian Mental Health Collective
- Canadian Directories
- British Directories
- Australian Directories
- New Zealand Directories