If I understand your question correctly, you want to create a Web Data Connector around a RESTful service that is protected by OAuth2.
A roundabout way of doing things would be to authenticate to that OAuth2 resource yourself and save the access_token given by the OAuth2 provider and use that directly in your Web Data Connector as that is all the OAuth2 requires you to use to authenticate.
These access_tokens can and will expire though, so every time you used the connector you'd need to specify a new token.
Alternatively, you could add an OAuth2 library (there are many and you can see a list here: OAuth 2.0 — OAuth) under 'Client Libraries' for whatever language you're writing your connector in and have your connector authenticate for you.
Because OAuth2 relies on the 'GET' HTTP protocol this will even work for a local server that the Web Data Connector creates!
I hope this helps.