There is no direct way to do this.
But if you really want to give it a try, then you will need to read the JOptionPane API which gives code that shows you how to manually create and display a JOptionPane without using the showXXX methods.
Using this approach you now have access to the actuall JDialog. Then you can use Darryl's SwingUtils to access the individual buttons and then set the background.
The code would be something like:
JButton ok = SwingUtils.getDescendantOfType(JButton.class, dialog, "Text", "Ok");
ok.setBackground(...);
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