標準の TreeView を拡張バージョンに置き換えようとしたときに、この例外が発生しました。単純なプロジェクトを作成したことを単純化するためです。確かに簡単な解決策があります。
例外:
Can not set testtreeviewwithitems.MyTestTree field testtreeviewwithitems.Sample.treeView to javafx.scene.control.TreeView
/C:/Users/Vlad/Documents/NetBeansProjects/TestTreeViewWithITems/build/classes/testtreeviewwithitems/Sample.fxml:10
  at sun.reflect.UnsafeFieldAccessorImpl.throwSetIllegalArgumentException(UnsafeFieldAccessorImpl.java:164)
  at sun.reflect.UnsafeFieldAccessorImpl.throwSetIllegalArgumentException(UnsafeFieldAccessorImpl.java:168)
  at sun.reflect.UnsafeObjectFieldAccessorImpl.set(UnsafeObjectFieldAccessorImpl.java:81)
  at java.lang.reflect.Field.set(Field.java:680)
  at javafx.fxml.FXMLLoader$ValueElement.processValue(FXMLLoader.java:659)
  at javafx.fxml.FXMLLoader$ValueElement.processStartElement(FXMLLoader.java:572)
  at javafx.fxml.FXMLLoader.processStartElement(FXMLLoader.java:2314)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2131)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2028)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2742)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2721)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2707)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2694)
  at javafx.fxml.FXMLLoader.load(FXMLLoader.java:2683)
  at testtreeviewwithitems.TestTreeViewWithITems.start(TestTreeViewWithITems.java:25)
  at com.sun.javafx.application.LauncherImpl$5.run(LauncherImpl.java:319)
  at com.sun.javafx.application.PlatformImpl$5.run(PlatformImpl.java:206)
  at com.sun.javafx.application.PlatformImpl$4.run(PlatformImpl.java:173)
  at com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
  at com.sun.glass.ui.win.WinApplication.access$100(WinApplication.java:29)
  at com.sun.glass.ui.win.WinApplication$2$1.run(WinApplication.java:67)
  at java.lang.Thread.run(Thread.java:722)
サンプル.java:
package testtreeviewwithitems;
import java.net.URL;
import java.util.ResourceBundle;
import javafx.fxml.FXML;
import javafx.fxml.Initializable;
public class Sample implements Initializable {
 @FXML
 private MyTestTree taskTreeView = new MyTestTree();
 @Override
 public void initialize(URL url, ResourceBundle rb) {
 } 
}
TestTreeView.java:
package testtreeviewwithitems;
import javafx.application.Application;
import javafx.fxml.FXMLLoader;
import javafx.scene.Parent;
import javafx.scene.Scene;
import javafx.stage.Stage;
public class TestTreeView extends Application {
    public static void main(String[] args) {
    Application.launch(TestTreeView.class, args);
    }
    @Override
    public void start(Stage stage) throws Exception {
        Parent root = FXMLLoader.load(getClass().getResource("Sample.fxml"));
        stage.setScene(new Scene(root));
        stage.show();
    }
}
MyTestTree.java:
package testtreeviewwithitems;
import javafx.scene.control.TreeView;
public class MyTestTree extends TreeView {
}
サンプル.fxml:
<?xml version="1.0" encoding="UTF-8"?>
<?import java.lang.*?>
<?import javafx.scene.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?>
<AnchorPane id="AnchorPane" prefHeight="200.0" prefWidth="320.0" xmlns:fx="http://javafx.com/fxml"     fx:controller="testtreeviewwithitems.Sample">
  <children>
    <TreeView fx:id="treeView" editable="true" focusTraversable="false" layoutY="0" prefHeight="50.0" prefWidth="100.0" showRoot="false" />
  </children>
</AnchorPane>
Java バージョン:
java version "1.7.0_11"
Java(TM) SE Runtime Environment (build 1.7.0_11-b21)
Java HotSpot(TM) 64-Bit Server VM (build 23.6-b04, mixed mode)
更新:解決策を見つけたようです。後で回答を投稿します。