I've got a set for Zapdos that I think could work.
@Life Orb
Naughty / Lonely; 252 Atk / 80 SpA / 176 Spe
Roost
HP Grass
Drill Peck
Thunderbolt
This set focuses on taking out two of Zapdos' biggest counters, namely Swampert and Blissey. Thunderbolt is a staple on any Zapdos set, allowing it to hit relatively hard with STAB Thunderbolt boosted by a Life Orb. Hidden Power Grass allows Zapdos to remove any and all Swampert that attempt to wall the set, as well as providing general coverage on other ground types. Drill Peck, however, forms the crux of the set. With it, Zapdos is able to 2HKO Calm 0 / 252 Blissey with it 100% of the time with Stealth Rock, and 70.94% of the time factoring in Leftovers, something that none of the other Zapdos sets can accomplish. While the set doesn't hit as hard as MS Zapdos or the LO + 3 Attacks set, it removes Blissey and allows Zapdos to proceed to fire powerful Thunderbolts at will. Roost adds longevity to the set, healing off LO damage incurred.
The EVs serve a specific purpose. Naughty nature is recommended over Lonely to allow Zapdos to retain the physical bulk granted by its typing and to better resist priority attacks, and along with maximum EV investment in attack it is able to 2HKO Blissey with stealth rock, as well as 252 / 220 Bold Celebi without it. 176 speed EVs allow Zapdos to outpace all neutral speed base 90s, such as Lucario. The rest of the EVs are placed into SpA to allow Zapdos to hit as hard as possible with Thunderbolt, and it allows HP Grass to OHKO Swampert 87.18% of the time with Stealth Rock. If more speed is desired, a simple 252 Atk / 252 Spe / 6 HP spread could be used, although Swampert is now OHKOd only 53.85% of the time after Stealth Rock.
The set is not without its flaws, however, as several pokemon can interfere with Zapdos' success. Tyranitar, Snorlax, Jolteon, Flygon, Gliscor, and Latias all cause the set problems. A Swampert of your own is well-equipped to deal with Tyranitar, Flygon, Gliscor, and those Jolteon that don't carry HP Grass. Scizor is also a good teammate to pair with Zapdos, resisting Ice attacks aimed at it, taking neutral damage from Rock, and having a powerful CB U-Turn or Bullet Punch to deal with the aforementioned threats. As an added bonus, it can trap and kill Latias with Pursuit. Yet another option is Metagross - its defensive synergy with Zapdos allows it to easily switch into stone edges or Ice Beams, using the appropriate attack to deal with the aforementioned pokemon. Offensively speaking, Zapdos is best paired with pokemon that will appreciate having Swampert and Blissey out of the way. A plethora of special attackers fall under this category, since Blissey is often the opponents only answer to special offense. Agility SubPetaya Empoleon is such an example, as well as Celebi, Heatran, or Starmie. Special mention goes to Jolteon, as the removal of Swampert allows it to run HP Ice alongside Thunderbolt with little worry, espcially when backed by a Life Orb or Choice Specs.