Actually such params as password and client id need to be passed as POST params, not GET params, from your documentation it isn't clear how POST params are passed, however, it maybe POST params are passed automatically.  

To generate key&secret with different grant type you need to generate it usual way in OAuth2 module, then you need to update some params manually via DB:

UPDATE bx_oauth_clients SET grant_types='password' WHERE client_id='<your client id>';
UPDATE bx_oauth_clients SET client_secret='' WHERE client_id='<your client id>';

Then you will be able to get access token using the following CURL command:

curl -X POST "https://you-una-site-domain/modules/?r=oauth2/token" -d "grant_type=password&scope=basic&client_id=<your client id>&username=<your login email>&password=<your login password>"

So try to set the following in your config:

oauth_client_id = "<your client id>"
oauth_client_secret = ""
oauth_url = "https://you-una-site-domain/modules/?r=oauth2/token";
authentication = "oauthbearer"

oauth_client_secret is empty when password grant type is used

If it will not work, ask them for the support, or they need to provide more complete documentation.