I'd try something like:
public static Bitmap mergeImages(Bitmap bottomImage, Bitmap topImage) {
final Bitmap output = Bitmap.createBitmap(bottomImage.getWidth(), bottomImage
.getHeight(), Config.ARGB_8888);
final Canvas canvas = new Canvas(output);
final Paint paint = new Paint();
paint.setAntiAlias(true);
canvas.drawBitmap(bottomImage, 0, 0, paint);
canvas.drawBitmap(topImage, 0, 0, paint);
return output;
}
(not tested, I just wrote it here, might be some simple errors in there)
Basically what you do is create a 3rd empty bitmap, draw the bottom image on it and then draw the top image over it.
As for saving to a file, here are a few examples: Save bitmap to location