Noivern always felt as a counterpart to Crobat, being a similar fragile speedster Bat pokémon. The even have similar Base Stats, with Noivern sacrificing 7 Speed for 7 higher in its main offensive stat. However, Noivern is by far the more offensive of the two, having great spammable STABs and an absurd coverage move in Boomburst, in addition to just wide coverage in general. Sadly, Noivern really wishes it had access to Nasty Plot to boost its offenses, instead being reliant on Choice Specs for extra damage. Additionally Noivern's typing thrusts it into competition with numerous Dragon types who offer similar defensive niches and shortcomings while often offering far better bulk and power.
Other Options
Super Fang -always valuable for cleaving past walls with more defense than sense, but Noivern excels as a revenge killer, not as a wall breaker.
Taunt -shuts down setup attempts, and synergizes well with Super Fang for weakening walls by preventing them from recovering.
Checks and Counters
Noivern is comparable with other Dragon types for having similar achilles heels. STAB Ice moves will drop Noivern quickly and it doesn't have Intimidate, Multiscale or the bulk like Garchomp to tank an Ice move. Ice Shard from the likes of Weavile or Mamoswine quickly ends Noivern's threat before it can begin.
Weavile in general is a huge headache for Noivern, being a naturally faster Ice type, though obviously Weavile can't switch into Noivern safely. Other faster threats like Dragapult, Regieleki, and Ribombee all naturally outspeed and threaten to OHKO Noivern.
Otherwise, taking advantage of Noivern's middling special offense works wonders. Blissey and Chansey just sit on Noivern, but must be wary of sets with Super Fang and Taunt. Specially defensive Celesteela works well against sets lacking Choice Specs and Flamethrower/Thunderbolt. Umbreon is another hard wall, but again hates Taunt. Snorlax, Porygon2, Stakataka, Bronzong all have the special Bulk required to take a few hits from Noivern and threaten it back hard, though Choice Specs sets will begin to strain this.