I came across this library:
https://github.com/cassiozen/corona-googleConnect/blob/master/googleConnect.lua
And so far so good, but if you look at lines 89 and 90, it has listed as ‘to-do’ checking the values returned. Since I don’t know how the oauth2 code works, I can’t actually explore this.
I know people have been asking for oauth2 login (I am using it for gmail), I thought I’d stick this up to see if better minds than mine can help - I’d rather find out problems before I release an app using it 
Barry