How can we get a new court appointed lawyer?

Unlike firing a paid attorney, you need a reason to fire your public defender. The fact that you don't like him or do not feel (s)he is doing a good job for you may not be enough. A judge is more likely to permit you to change public defenders if your current lawyer is somehow violating your right to adequate representation. Some evidence of that could be: (5) Missing appointments or filing deadlines, (6) Not informing you about your case status or hearing dates, (7) Forcing you to enter a plea, or (8) Ignoring important evidence. To change your public defender, you generally need to write a letter to the judge in your case or contact the public defender's office, depending on the rules in your state. Make sure you keep good notes of what you believe to be the biggest problems with your attorney. There's a chance a judge will grant your request if you have good reason to change public defenders. But they're unlikely to grant a second request, so make sure you really do need a new lawyer. Before you file any paperwork, make sure that you talk to your current public defender. Sometimes the issue isn't that your attorney isn't doing the work, it's a communication problem. Tell your attorney about what is making you unhappy, and see if something can be done to change it.

The defendant has to ask the judge for a new lawyer. Or you can go and hire one for him.

I don't know whether or not you have sufficient grounds, however, the defendant would have to be the one to file a motion for this with the court. The Judge will determine the merits or lack thereof of the motion.