Tyranitar is difficult to counter because it can use so many different moves, but these Pokemon will usually work.
Ground Pokemon like Swampert and Hippowdon resist rock and hit back with a super effective earthquake.
Fighting Pokemon like Machamp and Breloom resist both STABs, and their fighting attacks are quadruple effective.
Scizor and Bronzong resist one of Tyranitar's STABs and are not weak to earthquake, and their steel attacks are super effective.
Skarmory, Blissey, Forretress, and Lucario are good counters when Tyranitar is choice locked to a weak move.
Dragonite is another Pokemon that learns many moves and is not very predictable.
Skarmory and Hippowdon can usually take a hit and then use roar or whirlwind.
Scizor resists extreme speed, and its bullet punch hits before Dragonite's other moves.
Mamoswine can use ice shard, but it must watch out for extreme speed.
Threats to Bronzong:
Water Pokemon like Gyarados, Starmie, and Swampert resist gyro ball, and their water moves get STAB and are neutrally effective.
Steel Pokemon like Skarmory, Scizor, and Lucario resist gyro ball and explosion and are immune to toxic.
Slow Pokemon like Nidoqueen and Hippowdon take little damage from gyro ball and can use protect to stall against trick room and screens.
Threats to Machamp:
Gyarados can intimidate Machamp and resist dynamic punch.
Forretress can usually tank dynamic punches, remove stealth rock for Gyarados, and set up its own stealth rock.
Lapras and Alakazam are so easy to check that they aren't ranked. A good team will usually unintentionally include good checks for these Pokemon.
First, put Gyarados on your team. It is the best Pokemon that can check Machamp and counter another opponent, and its intimidate can help against Tyranitar and Dragonite. Use Hippowdon to check fire blast Tyranitar and defensive Dragonite and Scizor to check ice beam Tyranitar and offensive Dragonite. I recommend using Breloom just because Tyranitar is that difficult to check. Then you can add Clefable for support and Gengar for type coverage. These are the movesets I recommend. Make sure Hippowdon is first to set up stealth rock quickly. The order of the other Pokemon doesn't matter.
Hippowdon @ leftovers
EVs: 252 HP / 252 Def / 4 SpD
- stealth rock
- slack off
- ice fang
Gyarados @ leftovers
EVs: 252 Atk / 4 Def / 252 Spe
- dragon dance
- stone edge
Scizor @ choice band
EVs: 248 HP / 252 Atk / 8 SpD
- bullet punch
Breloom @ toxic orb
Ability: poison heal
EVs: 12 HP / 244 Atk / 252 Spe
- focus punch
- stone edge
Clefable @ leftovers
Ability: magic guard
EVs: 252 HP / 4 Def / 252 SpD
- thunder wave
- knock off
- seismic toss
Gengar @ black sludge
EVs: 80 HP / 176 SpA /252 Spe
- shadow ball
- focus blast
All 6 of these Pokemon are obtainable in HGSS.