Cold emails is #1 best way to market a new SaaS product because its free and you get to hear feedback from customers. Aside from that "marketing" is really just building a list of a bunch of different tactics and trying each of them until you find something that works.

I once wrote on how a team I was on drove a bundle of users to a new app. It may give you some inspiration: http://www.entrepreneur.com/article/237922

I happy to brainstorm ideas with you if you ping me on twitter @jsfour