Nick Fury is out. He's not a part of SHIELD anymore.
When Coulson died and was brought back he was "officially" dead, but still registered as a SHIELD agent for those who were in on the secret, like Fury and Maria Hill. He still took orders, received equipment, went out on missions, etc.
When Nick Fury "died," he cut all ties to SHIELD. Coulson was made Director at the end of the first season of AoS, and while he knows Fury is alive, Fury isn't (to the best of our knowledge) working with him or even in contact. Even in the Season 1 finale, Fury showed up to help in more of a "favor for a friend" sort of way, not as an official operative.
So, until Age of Ultron or some other MCU story says different, we have to assume that Nick Fury has cut all ties to SHIELD, is officially dead in the public record, and is "disavowed" or completely disassociated with Coulson.
EDIT: There seems to be some confusion about the timing of my answer. According to my understanding, there are four phases of SHIELD's recent leadership, and I've elaborated Nick Fury's "current position in SHIELD" for each:
- Before Winter Soldier - SHIELD is strong, Nick Fury is in command and everyone knows it.
- During Winter Soldier - SHIELD is in utter disarray. Nick Fury is believed dead, so the official Director is whatever next-level officer was in line to succeed him, but Nick Fury is still pulling the strings and commanding certain elements within SHIELD.
- Winter Soldier to AoS Season 1 Finale - SHIELD officially still exists but has been branded a terrorist organization. The official Director is unknown (likely changing or in dispute between several SHIELD and HYDRA agents), and the chaos is so great that there is no "practical" leader of SHIELD at all. Nick Fury is still alive, but seems to have cut ties with SHIELD and is no longer maintaining contact with any SHIELD agents or operations.
- After AoS Season 1 - Nick Fury resurfaces for long enough to give Coulson the intel and resources he'll need to rebuild SHIELD, then disappears again. We see no further indications of him contacting or working with Coulson, May, Hill, Romanov, or any other SHIELD or ex-SHIELD elements. It's unlikely he "made it official" when he named Coulson as Director (since he's supposed to be dead and thus doesn't get a vote), but with the resources he gave Coulson, it wouldn't be hard for Coulson to assert authority over any rival leadership that had sprung up during the interregnum. Thus, the "official" Director of SHIELD was probably in flux for a while, and simply settled on Coulson eventually.
So, to answer your question, the "current" position of Nick Fury during Season 2 of AoS could be stated as "Officially dead, Effectively retired/discharged." To the best of our knowledge, he has no more ties to SHIELD than a retired General does to the Army. He's out, both officially and practically.