Authenticate using OAuth
I think you're desire to use Oauth is justified. However, if you have no other options, you can use Cookie authentication. I have used it before and have heard of people using it as well. Here are some things to keep in mind and you'd be good to go with Cookie auth with your mobile application:


You will have to increase the session timeout time to a long period, say, 1 year or more. This means that after the period, the user would have to be asked to login again. Alternatively, you can refresh the Cookie with each request. You will need to:


Change session settings in PHP settings
Change session settings in Drupal settings

You will have to authenticate the user and then have a mechanism to persist the user's Session ID using a Set-Cookie header.
You will need to have a mechanism to handle sign-in failure when the session cookie has expired. When the session expires, you can send the user to the sign-in page again (maybe with the username field pre-populated) and ask then to sign-in again.
Since leaving a session long open poses to be a security threat, you might consider using other mechanisms like CSRF tokens.


Note: If you are in the mood for experimentation, you can also look into JWT authentication. Also, if you expect to have a huge user-base, you might consider a service like Firebase for storage.

Hope it helps. Happy coding!