If you want EV training and all that competitive stuff, then you'll probably have to hatch Zigzagoon which I believe you don't want to do and just use ones from Wonder Trade. Anyway, I would suggest one HM slave like so:
This one can be fainted and the first in your party to pick up items and for an HM slave.
Zigzagoon @ nothing (Pickup)
- Rock Smash
- Strength (only if its a Linoone :c)
The other Zigzagoon should be attackers of course and could have this as a suggested moveset:
Zigzagoon @ Sitrus Berry
- Belly Drum
- Double Edge / Return
- Seed Bomb / Gunk Shot
Good coverage and belly drum is great with Sitrus Berry. Double Edge is a strong normal type move but Return can work for a solid STAB move if you have good friendship. For EVs, (optional) give it some Speed, Attack, and HP. For the last move, those two options are only if you have a move tutor available. If not, choose Pin Missile.
If you'd like to catch some Pokemon then give one of them Super Fang to gradually wear down their HP and maybe have Charm to lower attack or Captivate if you're a girl and they're a special attacker. Have fun with this team and may you defeat many Mega Rayquazas!
P.S. My bro has a shiny Zigzagoon with Pokerus!