Since your users have a Google Apps for Business email address already, I would suggest using the Google+ Federated Login feature-set. (You can learn more here: https://developers.google.com/accounts/docs/OpenID)
A quick snippet from the aforementioned link:
If you are planning to provide a “sign-in with Google” feature, we recommend using Google+ Sign-in, which provides the OAuth 2.0 authentication mechanism along with additional access to Google desktop and mobile features...[the] OpenID+OAuth Hybrid protocol lets web developers combine an OpenID request with an OAuth authentication request. This extension is useful for web developers who use both OpenID and OAuth, particularly in that it simplifies the process for users by requesting their approval once instead of twice.
You can find more on the Google+ Federated Login toolset and explore a sample application here: https://developers.google.com/+/
Hope this helps!