Look at the attached movie.

Use code to reproduce this:

import java.util.Random;
import javafx.application.Application;
import javafx.collections.FXCollections;
import javafx.collections.ObservableList;
import javafx.event.Event;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.chart.*;
import javafx.scene.control.*;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Pane;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;

public class JavaCharts extends Application {

    public static void main(String[] args) {
        launch(args);
    }
    NumberAxis axisY = new NumberAxis(0, 100, 10);
    ObservableList<String> existingCategories = FXCollections.observableArrayList();
    CategoryAxis axisX = new CategoryAxis(existingCategories);
    StackedBarChart testedStackedBarChart = new StackedBarChart(axisX, axisY);
    VBox vb = new VBox();

    @Override
    public void start(Stage stage) throws Exception {
        testedStackedBarChart.setTitle("BarChart");
        testedStackedBarChart.setStyle("-fx-border-color: darkgray;");
        existingCategories.addAll("category1", "category2", "category3");

        addData();

        Pane pane = new Pane();
        pane.setPrefSize(600, 600);

        pane.setPrefSize(600, 600);
        pane.getChildren().add(testedStackedBarChart);

        vb.getChildren().addAll(pane, getAddItemHBox(), getAddCategoryDialog(), getRemoveCategoryDialog());

        Scene scene = new Scene(vb, 700, 700);
        stage.setScene(scene);
        stage.show();
    }

    public void addData() {

        String serieName = "Serie";
        double min = 0;
        double max = 100;
        int amount = 3;

        ObservableList list = FXCollections.observableArrayList();

        XYChart.Series serie = new XYChart.Series(serieName, list);

        for (int i = 0; i < amount; i++) {
            XYChart.Data newData = new XYChart.Data();
            String category = existingCategories.get(i);
            Double value = new Random().nextDouble() * (max - min) + min;
            newData.setYValue(value);
            newData.setXValue(category);
            list.add(newData);
            System.out.println(newData + " to category " + category + " value " + value);
        }

        testedStackedBarChart.getData().add(serie);
    }

    public HBox getRemoveCategoryDialog() {
        HBox hb = new HBox();
        Label lb = new Label("From index");
        final TextField tf = TextFieldBuilder.create().text("0").prefWidth(50).build();
        Button bt = ButtonBuilder.create().text("Remove category!").build();
        bt.setOnAction(new EventHandler() {

            @Override
            public void handle(Event t) {
                int index = Integer.parseInt(tf.getText());
                existingCategories.remove(index);
                axisX.getCategories().remove(index);
            }
        });
        hb.getChildren().addAll(lb, tf, bt);
        return hb;
    }

    public HBox getAddCategoryDialog() {
        HBox hb = new HBox();
        Label lb = new Label("Category");
        final TextField tf = TextFieldBuilder.create().text("").prefWidth(50).build();

        Label lind = new Label("to index");
        final TextField tfind = TextFieldBuilder.create().text("0").prefWidth(50).build();

        Button bt = ButtonBuilder.create().text("Add!").build();
        bt.setOnAction(new EventHandler() {

            @Override
            public void handle(Event t) {
                int index = Integer.parseInt(tfind.getText());
                existingCategories.add(index, tf.getText());
                axisX.getCategories().add(index, tf.getText());
            }
        });
        hb.getChildren().addAll(lb, tf, lind, tfind, bt);
        return hb;
    }

    public HBox getAddItemHBox() {
        HBox hb = new HBox();
        Label lb = new Label("Add series named ");
        final TextField tf = TextFieldBuilder.create().prefWidth(50).id("Named").build();

        Label minLabel = new Label(" min ");
        final TextField minText = TextFieldBuilder.create().prefWidth(50).build();

        Label maxLabel = new Label(" max ");
        final TextField maxText = TextFieldBuilder.create().prefWidth(50).build();

        Button bt = ButtonBuilder.create().text("Add!").build();
        bt.setOnAction(new EventHandler() {

            @Override
            public void handle(Event t) {
                String serieName = tf.getText();
                double min = Double.parseDouble(minText.getText());
                double max = Double.parseDouble(maxText.getText());

                ObservableList list = FXCollections.observableArrayList();

                XYChart.Series serie = new XYChart.Series(serieName, list);

                for (int i = 0; i < 3; i++) {
                    XYChart.Data newData = new XYChart.Data();
                    String category = existingCategories.get(i);
                    Double value = new Random().nextDouble() * (max - min) + min;
                    newData.setYValue(value);
                    newData.setXValue(category);
                    list.add(newData);
                    System.out.println(newData + " to category " + category + " value " + value);
                }

                testedStackedBarChart.getData().add(serie);
            }
        });
        hb.getChildren().addAll(lb, tf, minLabel, minText, maxLabel, maxText, bt);
        return hb;
    }
}

To add new data: type name of serie, type minimalX, type maximalX, click button.
To remove category (with according data from chart): type index and click according button.
To add category: type name, type index to add, click button.