What you want to do is to override paintComponent(Graphics g)
in your JRoundedButton class and do all the painting yourself there.
Kind of:
class JRoundedButton extends JButton
{
   public void paintComponent(Graphics g)
   {
       int radius = 10;
       g.setColor(getBackground());
       //here comes your round button
       g.fillOval(0,0,getWidth(),getHeight(),radius,radius);
       //and now obtain text of the button, calculate its position
       //regarding aligning and paint it with foreground color
   }
}

That way you would have the same look of your round buttons
regardless of used L&F. I'd say it is not the best idea.

I would suggest creating a Border implementation
that would just take care of rendering round border
around your buttons.
Whenever you'd want a round button you would
setBorder(new MyRoundBorder())
on the one that you want to be round.

So you would not have to do all the rendering yourself,
just the border. And your RoundBorder could use
settings of the current L&F.

HTH,
Adam

java.awt.geom.Class RoundRectangle2D could help you.
you can also use it to set the clip of Grapihcs while painting.