Mixed sweeping flying types in NU...you're already pretty limited in that sense since a lot of NU pokes don't really have too many options to begin with. If you have spin support, Charizard is probably your best bet, it runs a mixed set quite well and has access to Roost as well. There are a ton of other NU Flying types to choose from, but once again most are focused on either attack or special attack.
You'll have to excuse my lack of knowledge of the NU metagame, I haven't made an NU team in quite a while. But in general, I'd definitely have a counter for physically based Cacturne and Ursaring, who I've heard are quite monstrous in NU. Anything choiced with a high attack stat can also do damage, like Kingler, Armaldo, Pinsir, ect. While of course you can play around these prediction, I'd make sure you have a nice steady physically bulky pokemon on your team, or at least something that can outspeed them comfortably.
On the special side, Exeggutor, Magmortar, Ampharos, Cacture again, Jynx, ect are capable of causing some damage. Same thing with these, they can all be played around with good prediction, but be prepared for them. If you need specifics on any of these, just let me know.