You'll find a lot of info out there about CTA tests and theories. But you're not going to find a whole lot that tells you what to do with horizontal alignment. The reason is, it depends on your design.
If your colleagues want to talk about what is more common, then you should align right, as you suggest. This is used more often than left because it denotes moving forward in a sequence (at least for us left-to-righters). Conversely, you'll find a lot of "< Back to something" CTAs aligned left.
Fitting the context
In your case, the site content is mostly centered, which trains the user to move along the central vertical axis. It also creates an aesthetic environment that favors symmetry. In that context, I would center align the button. For the visually minded, here's a quick wireframe of following the dominant axis of alignment.
Finding the problem
If you're having trouble with users missing a centered button, you have to ask yourself if you've given it proper scale, spacing, and differentiation from the surrounding view. As I'm sure you know, alignment is not the only factor in play.
More importantly, do you know for certain that it's being missed? Sometimes a lack of clicks is not for lack of visibility. Do users know what to expect when they click? Have you given them adequate motivation?
Not that it means much, but here's confirmation that centered can work from Smashing Mag.
Locating a call to action button in the middle of a web layout with no
(or significantly smaller and deemphasized) flanking elements can be
an effective way of drawing attention and enticing an action.