Answeri your question, I'd lead with Garchomp. If you know anythig about Garchomp or Dragon types in general, it would be that they have some fantastic offensive firepower. Even better, they have access to a ton of moves with different types. You can teach Garchomp Poison Jab, Earthquake, Aqua Tail, Stone Edge, or whatever suits it best. Anything your Garchomp lacks can be made up with Dragonite.
If Garchomp were to faint (this would usually be to an Ice type, or something with Ice Beam or Punch), you would want Arcanine to finish it off with Flare Blitz or some Fire type attack. Arcanine has some good Speed (or should I say ExtremeSpeed, which is an awesome move that you should carry on Arcanine) and a mix of Special Attack and regular Attack. Like your Dragons, Arcanine can learn a variety of different-typed moves.
If Arcanine goes down, send in Gyarados. You're usually dealing with a Ground type Pokemon. which Gyarados can handle with Ice Fang, Aqua Tail, or some Special Attacks like Surf, even though I wouldn't recommend Surf.
If Gyarados falls, there is an Electric or Rock type Pokemon you have to take down. In this situation, you would want Tyranitar to Earthquake or some other moves like Ice Punch.
This team needs some more type diversity and Pokemon that know Special Attacks (like an Espeon, Gengar, Alakazam.). Magnezone is good, but it can't do all of the Special Attacking alone.
I wouldn't worry too much because even though Diamond is one of the more difficult Pokemon games, you're still going up against CPU opponents who won't always use moves that will destroy your team in one hit. You did say you played Diamond before, so you should have an idea of what to expect.