Educational background in kinesiology and/or exercise science is a great indicator of a qualified running coach.
There are several organizations that provide certification programs for running coaches as well. Some of the prominent running coach certifications to look for are the Road Runners Club of America (RRCA), Jack Daniels VDOT, Lydiard School of Coaching, and USATF. Each of these certifications is slightly different in style and method so it would be advisable to do some research and decide what will work best for your training needs.
There are also certifications such as the NASM and ACE which provide various certifications for fitness professionals who may or may not specialize in training runners.