To copy selected table rows, you can use Java's built-in support:

TransferHandler th = myTable.getTransferHandler();
if (th != null) {
    Clipboard cb = Toolkit.getDefaultToolkit().getSystemClipboard();
    th.exportToClipboard(myTable, cb, TransferHandler.COPY);
}

If you want to copy the entire table contents, you probably have to
write it yourself. Have a look at the source code of the nested class
TableTransferHandler in javax.swing.plaf.basic.BasicTableUI.