Does anyone know of any clinical psychology journals that use a double-blind review process?
My impression is that many (perhaps most) psychology journals do double-blind review (or at least give you the option). 

Journal of Consulting and Clinical Psychology is one example.
http://www.apa.org/pubs/journals/ccp/?tab=4


  This journal uses a masked reviewing system for all submissions. 


It sounds like that (a) you are not aware of what clinical psychology journals exist in your area; and (b) how to determine whether they require or allow for masked review. I'll discuss each of these points.

Finding a relevant clinical psychology journal: If you are writing a journal article, you will need to perform a review of the literature. Identify journals from those that you cite in your references. There are also various lists of journals organised by topic (e.g., Science Citation Index) that often give an indication of journal prestige. If you are interested in clinical psychology, then you may also want to check out "psychiatry" journals as well.

Determining review policy. Every journal has a website, and a section of the website will include instructions to authors. Here you will typically find information about the reviewing process.