How To Do A Deep Copy Of Objects That Contain References

how to do a deep copy of objects that contain references. I am specifically wanting to make a deep copy of a tree. Logically, each tree node contain references to its children nodes. Here is the basics of my node class

public class BSTNode implements Comparable, Serializable {
 
private String token;
private int count;
private BSTNode leftChild;
private BSTNode rightChild;

I know I must only be making a shallow copy because when I make a copy of tree1, called tree2, and edit tree1 the edits also appear on tree2. Here is my copy method within my BSTNode class

public BSTNode copy()
{
BSTNode obj = null;
try{
ByteArrayOutputStream bos = new ByteArrayOutputStream();
ObjectOutputStream out = new ObjectOutputStream(bos);
out.writeObject(this);
out.flush();
out.close();

[code]....

When I wish to copy the entire tree, I call that above copy method from my BSTree class using the methods below. (I have 2 methods because this is a homework assignment that requires a copy method that calls a preorder traversal method)

public BSTNode copy()
{
BSTNode copiedTreeRoot = new BSTNode();
return copyTree(copiedTreeRoot,root);
 
[code]....

And further along when I make changes to tree1, tree 2 also changes. I have no clue what I'm doing wrong. I believe it must be somewhere in how I return the new tree or something.I tried this edit to my copy method, but it made no difference.

public BSTNode copy() {
BSTNode obj = null;
try{
ByteArrayOutputStream bos = new ByteArrayOutputStream();
ObjectOutputStream out = new ObjectOutputStream(bos);
out.writeObject(this);

[code].....