One would expect the scroll bar to be red. Change the child relationship to descendant and the selector matches.
Knowing that the skin is a child of the ScrollBar, .myParent > * > .scroll-bar should work but does not.

/*
 * demo.css
 */
.myParent > .scroll-bar {
    -fx-border-color: red;
}

package javaapplication37;

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.ScrollBar;
import javafx.scene.layout.AnchorPane;
import javafx.stage.Stage;

/**
 *
 * @author jfdenise
 */
public class JavaApplication37 extends Application {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Application.launch(args);
    }

    @Override
    public void start(Stage primaryStage) throws Exception {
        AnchorPane ap = new AnchorPane();
        ap.getStyleClass().add("myParent");
        ScrollBar sb = new ScrollBar();
        ap.getChildren().add(sb);
        
        Scene scene = new Scene(ap, 100, 100);
        scene.getStylesheets().add(JavaApplication37.class.getResource("demo.css").toExternalForm());

        primaryStage.setScene(scene);
        primaryStage.setVisible(true);
    }
}