[hardwired]

You will need to add a MouseListener to the BallCanvas and run through the BouncingBalls to see if the user has clicked on any of them. When you get a reference to a selected ball you can remove it from the BallCanvas list. The other detail is that each BouncingBall has an animation thread running. Ideally, we would stop and eliminate this as we remove the ball from the view (BallCanvas). I refactored the class structure/design to facilitate this.

Code:

import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.util.*;
import java.util.List;
import javax.swing.*;
 
public class BounceBallAgain extends MouseAdapter implements ActionListener {
    BallCanvas canvas = new BallCanvas();
    BouncingBall selectedBall = null;

    public void actionPerformed(ActionEvent e) {
        String ac = e.getActionCommand();
        if(ac.equals("ADD BALL"))
            addBall();
        if(ac.equals("DELETE BALL"))
            delBall();
        if(ac.equals("EXIT"))
            System.exit(0);
    }

    private void addBall() {
        BouncingBall bb = new BouncingBall(canvas);
        canvas.add(bb);
        bb.start();
    }

    public void delBall() {
        if(selectedBall != null) {
            selectedBall.stop();
            canvas.delBall(selectedBall);
            selectedBall = null;
            canvas.repaint();
        }
    }

    public void mousePressed(MouseEvent e) {
        Point p = e.getPoint();
        BouncingBall[] balls = canvas.getBalls();
        for(int j = 0; j < balls.length; j++) {
            if(balls[j].contains(p)) {
                if(selectedBall != null)
                    selectedBall.setSelected(false);
                selectedBall = balls[j];
                selectedBall.setSelected(true);
                break;
            }
        }
    }

    private JPanel getButtonPanel() {
        String[] ids = { "Add Ball", "Delete Ball", "Exit" };
        JPanel panel = new JPanel();
        for(int j = 0; j < ids.length; j++) {
            JButton button = new JButton(ids[j]);
            button.setActionCommand(ids[j].toUpperCase());
            button.addActionListener(this);
            panel.add(button);
        }
        return panel;
    }

    public static void main(String[] args) {
        BounceBallAgain test = new BounceBallAgain();
        test.canvas.addMouseListener(test);
        final int WIDTH = 450;
        final int HEIGHT = 350;
        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.getContentPane().add(test.canvas);
        frame.getContentPane().add(test.getButtonPanel(), "Last");
        frame.setSize(WIDTH, HEIGHT);
        frame.setLocation(200,200);
        frame.setVisible(true);
    }
}

class BallCanvas extends JPanel {
    private List<BouncingBall> balls = new ArrayList<BouncingBall>();

    public void add(BouncingBall b) {
            balls.add(b);
    }

    public void delBall(BouncingBall db) {
        balls.remove(db);
    }

    public BouncingBall[] getBalls() {
        int size = balls.size();
        return balls.toArray(new BouncingBall[size]);
    }

    public void paintComponent(Graphics g) {
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                            RenderingHints.VALUE_ANTIALIAS_ON);
        for (int i = 0; i < balls.size(); i++) {
            BouncingBall b = (BouncingBall)balls.get(i);
            b.draw(g2);
        }
    }
}
 
class BouncingBall implements Runnable {
    private Component canvas;
    private static final int XSIZE = 15;
    private static final int YSIZE = 15;
    private int x = 0;
    private int y = 0;
    private int dx;
    private int dy;
    Color color;
    boolean selected = false;
    Thread thread;
    boolean keepBouncing = false;

    public BouncingBall(Component c) {
        canvas = c;
        color = getColor();
        dx = getSpeed();
        dy = getSpeed();
    }

    public void draw(Graphics2D g2) {
        g2.setColor(color); 
        g2.fillOval(x,y,30,30);   // adds color to circle
        if(selected)
            g2.setPaint(Color.magenta);
        g2.drawOval(x,y,30,30);   // draws circle
    }

    public void start() {
        if(!keepBouncing) {
            keepBouncing = true;
            thread = new Thread(this);
            thread.setPriority(Thread.NORM_PRIORITY);
            thread.start();
        }
    }

    public void stop() {
        keepBouncing = false;
        if(thread != null)
            thread.interrupt();
        thread = null;
    }

    public void run() {
        try {
            while(keepBouncing) {
                move();
                Thread.sleep(50);
            }
        } catch(InterruptedException e) {
            System.out.println("interruption");
            keepBouncing = false;
        }
    }
    
    private void move() {
        x += dx;
        y += dy;
        if (x < 0) {
            x = 0;
            dx = -dx;
        }
        if (x + XSIZE >= canvas.getWidth()) {
            x = canvas.getWidth() - XSIZE;
            dx = -dx;
        }
        if (y < 0) {
            y = 0;
            dy = -dy;
        }
        if (y + YSIZE >= canvas.getHeight()) {
            y = canvas.getHeight() - YSIZE;
            dy = -dy;
        }
        canvas.repaint();
    }

    public boolean contains(Point p) {
        int w = 2*XSIZE;
        int h = 2*YSIZE;
        return new Ellipse2D.Double(x,y,w,h).contains(p);
    }

    public void setSelected(boolean selected) {
        this.selected = selected;
    }
    
    private Color getColor() {
        int rval = 50 + (int)Math.floor(Math.random() * 206);
        int gval = 50 + (int)Math.floor(Math.random() * 206);
        int bval = 50 + (int)Math.floor(Math.random() * 206);
        return new Color(rval, gval, bval);
    }

    private int getSpeed() {
        return 1 + (int)Math.floor(Math.random() * 4);
    }
}