File Db = new File("/data/data/your.package/databases/yourdatabasename");
Date d = new Date();

File file = new File("your_destination.db");
file.setWritable(true);

copyFile(new FileInputStream(Db), new FileOutputStream(file));

public static void copyFile(FileInputStream fromFile, FileOutputStream toFile) throws IOException {
    FileChannel fromChannel = null;
    FileChannel toChannel = null;
    try {
        fromChannel = fromFile.getChannel();
        toChannel = toFile.getChannel();
        fromChannel.transferTo(0, fromChannel.size(), toChannel);
    } finally {
        try {
            if (fromChannel != null) {
                fromChannel.close();
            }
        } finally {
            if (toChannel != null) {
                toChannel.close();
            }
        }
    }
}