Can I make my render method more efficient?
Sometimes, the correct answer really is "Nope; it's all good."  It makes for a boring answer, but there it is.  It doesn't look like you can make this much faster, based on what you've provided.

One thing you might consider is checking the variables to see if the image manipulations are actually needed before calling the respective methods.  So, for example, something like...

graphics.setTransform((AffineTransform) defaultTransform.clone());
if(rotation != 0.0) {
    graphics.rotate(rotation, center.x, center.y);
}
if(scale.x != img.getWidth() || scale.y != img.getHeight()) {
    graphics.scale(scale.x, scale.y);
}
//...


This might give you a bit of performance where you don't need to bother going down into the rotate() and scale() methods.

Also, is there any way you can get rid of that (AffineTransform) cast?  Probably not, but that would speed you up ever so slightly.