Вы можете начать с этого образца:
try {
File sd = Environment.getExternalStorageDirectory();
File data = Environment.getDataDirectory();
if (sd.canWrite()) {
String currentDBPath = "\\data\\{package name}\\databases\\{database name}";
String backupDBPath = "{database name}";
File currentDB = new File(data, currentDBPath);
File backupDB = new File(sd, backupDBPath);
if (currentDB.exists()) {
FileChannel src = new FileInputStream(currentDB).getChannel();
FileChannel dst = new FileOutputStream(backupDB).getChannel();
dst.transferFrom(src, 0, src.size());
src.close();
dst.close();
}
}
} catch (Exception e) {
// exception
}