Hey, got your PM, good first RMT, though I have a few suggestions to patch up some weaknesses,
Dragon Dance Gyarados (and other assorted Dragon Dancers)
Common Stall core (Blissey+Skarmory+Rotom-A)
Weak to Rotom-A
First off, Dragon Dancers in general will give you a very hard time, especially Offensive Gyarados. By coming in on Jolteon's signal beam, or Infernape's Close Combat, it can set up and sweep unhindered, as even Starmie is OHKOed after Stealth Rock by +1 Stone Edge. Other Dragon Dancers get similar set up opportunities, but you have Infernape to revenge them. Obviously, Infernape can't switch in safely into any of them, so one or two team members are guaranteed to die before Infernape comes into revenge. Suicune and Jolteon will also be problematic thanks to boosted Hydro Pumps/Ice Beam/HP Electric (after Calm Mind) and Specs/LO boosted Thunderbolt/HP Grass/Shadow Ball. Rotom-A itself can also be troublesome, especially the W Forme. It can fire off Hydro Pumps to keep Jolteon at bay, and Thunderbolt to hurt Infernape, Starmie and Dragonite.
Right off the bat, I think Jolteon is the most replaceable member on this team. You said in the team building section that you added it to repel Gyarados. I don't see how you're accomplishing this by locking yourself into Signal Beam. Instead, I think a Scarf Rotom-W would work better in its place. Its valuable ability to take damage from Gyarados, and KO it back, as well as doing plenty to Dragonite with HP Ice, and crippling Chesto Rest Kingdra with Trick, as well as other stat uppers, like Calm Mind Jirachi. Opposing Jolteon will also be hesitant to switch into Rotom because of Hydro Pump. Try a simple set of: 200 HP/56 Satk/252 Spe Timid Nature, Thunderbolt|Hydro Pump|Trick|HP Icel.
So now we need a check to DD Tyranitar, and Stall. Firstly I think Shaymin should be changed to the Offensive Leech Seed variant, With max Satk/Speed Seed Flare/HP Fire/Earth power/Leech Seed Timid, and Leftovers. This will give you something to push around stall with, and a great counter to Suicune, and other Bulky Waters, as well as Rotom-A, which prove to be annoying for the team. It can also work as a last resort vs Jolteon, and KO with Earth Power. Since we already have a Choice scarfer, make Infernape a Physically Mixed Ape with the following set: 252 Atk/64 Satk/192 Spe Naive nature, and Close Combat/Overheat/Mach Punch/U-turn. This will give you a great priority move vs Lucario and Tyranitar. Finally, change Starmie to the offensive Life Orb variant with max Satk/max spe, timid nature, same moveset as your current one, but Ice Beam over recover, and Hydro Pump over Surf with a Life orb. Between Starmie+Infernape, you can break down stall easily.
Leech Seed shaymin>over current
LO Starmie>Leftovers Starmie