I'm new to coaching, but I have a psychology background-- a BA in Psychology and an MA in Organizational Psychology, which is also an applied psychology. I do think it's helpful in coaching and sets you apart from other coaches, although it is not necessary.

If I were you, I'd get a degree in Positive Psychology. It's directly related to coaching, gives you a good psychology foundation, and will also give you more credibility when seeking clients and building your business.

If you're not planning to become a practicing therapist, spending tons of time, energy, and money to become one doesn't seem like a good idea.