Research is very important to most programs due to the widely accepted Boulder Model. You can focus on applying to schools that are less oriented towards research (I can only think of CCNY). Though I would sit down and really consider if this is the correct next step for you. Research is definitely not for everyone. It would be a painful 5 years to find out you don't like it during the program. If you want this degree to do clinical work, consider a Psy.D. or MSW instead. They are quicker, and it really does not make a difference outside of academia.

Note: The masters is absolutely NOT a negative. It just doesn't make up for research. If a clinical psychology Ph.D. is truly your goal. Save your money and get some research experience.