as mentioned in comment , This is not "automatically" and also is not possible for the Play Services Framework except via software piracy.
if ur application can run and only after that u need google play service functionality :
Just do these step:
1, Download file use Asynctask or Service. Solution here
2, Pass downloaded file to package installer.
Intent intent = new Intent(Intent.ACTION_VIEW);
intent.setDataAndType(Uri.fromFile(new File(Environment.getExternalStorageDirectory() + "/download/" + "app.apk")), "application/vnd.android.package-archive");
startActivity(intent);
It's simple set path to downloaded file and mime type. More detail here. You can also look to the right. There is a list of related questions like yours
answer comes from "Jul" in this post :
How to download & install .apk file in Android application?