Just looked up rhyperior on smogon.
COUNTERS
Barring boosted Megahorns and Focus Punches, Bronzong can shake off pretty much anything Rhyperior can throw his way and hit back with Grass Knot. Skarmory can't hurt Rhyperior, but can stall him out—especially the Choice Band set—provided it is faster by wasting Stone Edge's PP with Roost and simply Whirlwinding him away.
Swampert handles him decently and can bring him down with STAB Water attacks, with Surf or Hydro Pump being more effective than Waterfall as they hit the weaker of Rhyperior's defensive stats. Suicune also fares well if he can avoid a critical hit from Stone Edge.
Hippowdon can wear him down by alternating between Earthquake and Slack Off. Beware of Choice Banded or Swords Danced Avalanches though.
If you can get them in on either of his STAB moves, Breloom and Torterra handle him well. Both can fire off Seed Bomb, while the latter can also use the more powerful Wood Hammer. Flygon can also work somewhat, although like the previously mentioned Grass-types, be sure to avoid Ice attacks and repeated hits from Megahorn.