Internal padding for JTextArea with background Image

Use a custom border that extends AbstractBorder. Something like this:

Getting the exact shape & color is left as an exercise for the reader. 🙂

import java.awt.*;
import java.awt.geom.*;
import javax.swing.*;
import javax.swing.border.AbstractBorder;

class TextBubbleBorder extends AbstractBorder {

    private Color color;
    private int thickness = 4;
    private int radii = 8;
    private int pointerSize = 7;
    private Insets insets = null;
    private BasicStroke stroke = null;
    private int strokePad;
    private int pointerPad = 4;
    RenderingHints hints;

    TextBubbleBorder(
        Color color) {
            new TextBubbleBorder(color, 4, 8, 7);
    }

    TextBubbleBorder(
        Color color, int thickness, int radii, int pointerSize) {
            this.thickness = thickness;
            this.radii = radii;
            this.pointerSize = pointerSize;
        this.color = color;

        stroke = new BasicStroke(thickness);
        strokePad = thickness/2;

        hints = new RenderingHints(
            RenderingHints.KEY_ANTIALIASING,
            RenderingHints.VALUE_ANTIALIAS_ON);

        int pad = radii + strokePad;
        int bottomPad = pad + pointerSize + strokePad;
        insets = new Insets(pad,pad,bottomPad,pad);
    }

    @Override
    public Insets getBorderInsets(Component c) {
        return insets;
    }

    @Override
    public Insets getBorderInsets(Component c, Insets insets) {
        return getBorderInsets(c);
    }

    @Override
    public void paintBorder(
        Component c,
        Graphics g,
        int x, int y,
        int width, int height) {

        Graphics2D g2 = (Graphics2D)g;

        int bottomLineY = height-thickness-pointerSize;

        RoundRectangle2D.Double bubble = new RoundRectangle2D.Double(
            0+strokePad,
            0+strokePad,
            width-thickness,
            bottomLineY,
            radii,
            radii
            );

        Polygon pointer = new Polygon();

        // left point
        pointer.addPoint(
            strokePad+radii+pointerPad,
            bottomLineY);
        // right point
        pointer.addPoint(
            strokePad+radii+pointerPad+pointerSize,
            bottomLineY);
        // bottom point
        pointer.addPoint(
            strokePad+radii+pointerPad+(pointerSize/2),
            height-strokePad);

        Area area = new Area(bubble);
        area.add(new Area(pointer));

        g2.setRenderingHints(hints);

        Area spareSpace = new Area(new Rectangle(0,0,width,height));
        spareSpace.subtract(area);
        g2.setClip(spareSpace);
        g2.clearRect(0,0,width,height);
        g2.setClip(null);

        g2.setColor(color);
        g2.setStroke(stroke);
        g2.draw(area);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                JLabel l = new JLabel(
                    "The quick brown fox jumped over the lazy dog!");

                l.setBorder(new TextBubbleBorder(Color.MAGENTA.darker(),2,4,0));
                l.setOpaque(true);
                l.setBackground(Color.BLACK);
                JOptionPane.showMessageDialog(null, l);
            }
        });
    }
}