Maybe not. I think the closest you'll get to finding a good counter for the team would be Ferrothorn/Kartana. Since they resist Water and quad resist Grass, they're a perfect option for resisting the weaknesses stated above. However, they do have a quad weakness to Fire and a weakness to Fighting. The Fighting can be covered with Gliscor, but both Ferrothorn/Kartana and Scizor have a quad Fire weakness, which is dangerous to have even if it's resisted by Mantine and Barbaracle. So, in short, I think the closest you'll get to what you want from the team is either Ferrothorn or Haxorus, who has a counter for Dragon and Fairy type attacks in the form of Scizor, but it shares an Ice weakness that can be countered, but it is annoying to counter. So, in short, it will work but it's imperfect.
Of course, I may have missed something as well, so search for yourself, I suppose.