Dropbox itself doesn't have listings or recommendations of developers to hire (though there may be some in the forum here who can chime in). There also may be third party marketplaces online where you can search for developers to hire, but we can't recommend any in particular. I certainly see how that could be helpful though, so I'll send this along to the team as a request to offer some sort of recommendation/listing like that. I can't promise if or when this would be implemented though.
As for the authorization functionality itself, Dropbox issues short-lived access tokens, which expire after a few hours, and optional refresh tokens, which don't expire. Apps can get long-term access by requesting "offline" access, in which case the app receives a "refresh token" that can be used to retrieve new short-lived access tokens as needed, without further manual user intervention. Refresh tokens do not expire automatically and can be used repeatedly. You can find more information in the OAuth Guide and authorization documentation. There's a basic outline of processing this flow in this blog post which may serve as a useful example.
