A while back, I had reviewed a pretty good book "Agile Product Management with Scrum" by Roman Pichler. You should definitely read it cover to cover to learn about Agile software development and the Product Owner/Manager's role.
Now, it may be time to go one step ahead and become a Certified Scrum Product Owner (CSPO).
This certification is a basic two-day introduction to gathering requirements and delivering them to the scrum team in the format of user stories. After getting certified, you will also get access to the online forums, blogs and other resources that you can use to hone your story-writing skills. One advertised benefit is the ability to show potential employers your knowledge of Scrum. There are some other certifications associated with Agile development (Scrum Master, Scrum Developer, Scrum Coach etc.) which are of limited use in a Product Owner role. You can find more information on these with a simple Google search.
Alternatively, you can go for the PMI Agile Certified Practitioner (PMI-ACP)® certification. This looks like a rigorous training with a lot of pre-qualifications before you apply for the certification. However, if you are already PMP certified, then it may be easier to get this certification. Personally, I am not in favor of product managers going for a PMP certification, for the simple reason that product managers have a different role that project managers.
If you are an old-timer in the industry, you might remember how Rational OOAD and UML was a pretty big thing at one time. And to get business analyst roles, you had to be well versed in those tools. Now with teams going agile, these certifications may give you the edge, when you are out there, looking for a product manager/product owner role.
Do understand your own career aspirations, the costs associated with these courses and then make an informed decision on either of these certifications.