..

...

Layouts, layouts, *layouts*!

This example does not quite have the shape or size
you originally had, but it ostensibly works.

<sscce>
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import javax.swing.border.*;

public class DynamicScroll extends JFrame implements ActionListener{

  private int buttonCount = 0;
  private JButton jButton1;
  private JPanel jPanelInScrollPane;
  private JScrollPane jScrollPane1;

  public DynamicScroll() {
      setDefaultCloseOperation( JFrame.DISPOSE_ON_CLOSE );
      JPanel mainPanel = new JPanel( new BorderLayout(50,50) );
      mainPanel.setBorder( new EmptyBorder(50,50,50,50) );

      jPanelInScrollPane = new JPanel();
      jScrollPane1 = new JScrollPane(jPanelInScrollPane);
      jButton1 = new JButton("Add Button");

      // have you not learned layouts yet?!
      // 'null' layouts are the path to madness!
      // the only time you should be setting a
      // layout to null is for custom painting,
      // and designing a new layout manager..
      // considers - no, even then it is probably redundant
      //getContentPane().setLayout(null);
      jPanelInScrollPane.setLayout(new FlowLayout());

      //jScrollPane1.setViewportView(jPanelInScrollPane);
      mainPanel.add(jScrollPane1, BorderLayout.CENTER);
      //jScrollPane1.setBounds(40, 40, 320, 80);

      //jButton1.setText("Add Button");
      jButton1.addActionListener(this);

      mainPanel.add(jButton1, BorderLayout.SOUTH);
      //jButton1.setBounds(150, 170, 120, 23);

      setContentPane( mainPanel );
      pack();

  }

  public void actionPerformed(ActionEvent evt) {
     JButton newButton = new JButton("Button "+ buttonCount);
      //newButton.setBounds( buttonCount  * (100)+10, 5,  100, 50);
      jPanelInScrollPane.add(newButton);
      buttonCount ++ ;
      jPanelInScrollPane.repaint();
      jPanelInScrollPane.validate();

      // validate the frame
      validate();
  }

  public static void main(String args[]) {
      DynamicScroll ds = new DynamicScroll();

      ds.setSize(400,300);
      ds.setVisible(true);
  }
}
</sscce>

    jScrollPane1.validate();

import java.awt.FlowLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import javax.swing.BoxLayout;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JScrollPane;

public class DynamicScroll2 extends JPanel implements ActionListener{

    private int buttonCount = 0;
    private JButton jButton1;
    private JPanel jPanelInScrollPane;
    private JScrollPane jScrollPane1;

    public static void main(String args[]) {
        JFrame f = new JFrame("Dynamic Scroll 2");
        DynamicScroll2 ds = new DynamicScroll2();
        f.add(ds);
        f.setSize(400,300);
        f.setVisible(true);
    }

    public DynamicScroll2() {
        jPanelInScrollPane = new JPanel();
        jPanelInScrollPane.setLayout(
                new BoxLayout(jPanelInScrollPane, BoxLayout.LINE_AXIS));

        jScrollPane1 = new JScrollPane(jPanelInScrollPane);

        jButton1 = new JButton("Add Button");
        jButton1.addActionListener(this);

        setLayout(new BoxLayout(this, BoxLayout.PAGE_AXIS));
        add(jScrollPane1);
        add(jButton1);
    }

    public void actionPerformed(ActionEvent evt) {
       JButton newButton = new JButton("Button:"+ buttonCount);
        newButton.setBounds( buttonCount  * (100)+10, 5,  100, 50);
        jPanelInScrollPane.add(newButton);
        buttonCount ++ ;
        jScrollPane1.validate();
    }
}