One options is to use the assets folder to store files and then copy them to your private app data directory. Something like this should work. This copies a database, but you could adapt it to copy your zip files.
/**
* Copies your database from your local assets-folder to the just created empty database in the
* system folder, from where it can be accessed and handled. This is done by transfering
* bytestream.
* */
private void copyDataBase() throws IOException {
// Open your local db as the input stream
InputStream myInput = mContext.getAssets().open(DB_NAME);
// Path to the just created empty db
String outFileName = DB_PATH.toString();
// boolean success = DB_PATH.mkdirs();
// Open the empty db as the output stream
OutputStream myOutput = new FileOutputStream(outFileName);
// transfer bytes from the inputfile to the outputfile
byte[] buffer = new byte[1024];
int length;
while ((length = myInput.read(buffer)) > 0) {
myOutput.write(buffer, 0, length);
}
// Close the streams
myOutput.flush();
myOutput.close();
myInput.close();
}