Single Strike Counters
OU Staple. Resists both of Urshifu's STABs, has access to recovery in Wish, and can attack back with Moonblast.
It's certainly underrated, but it has access to priority recovery in Triage Draining Kiss, which will go before Urshifu gets to attack. It doesn't match up against the rest of the meta-game very well, though.
Priority STAB Brave Bird. Even if you don't have your Gale Wings due to prior chip damage, you still have the natural speed available to outspeed Urshifu, unless Urshifu has a Choice Scarf (which is very uncommon anyways).
Bulky fairy type that is also immune to Poison Jab. If Urshifu goes for a Wicked Blow, then it's basically a single free turn of setup for Magearna (mostly to use Shift Gear).
Most Single-Strike Urshifu tend to run Adamant for the extra power, so if you are willing to give up a little power, you can use Jolly to guarantee outspeed them. Choice Scarf is probably sacrificing too much power for Urshifu to be usable. Dark Fighting also 4x resists Dark, so it's a Wicked Blow switch in if you feel risky.
Rapid Strike Counters
Rapid Strike Urshifu is a little more unpredictable, so it's hard to say if there is a designated counter.
Bulky Grass type that can handle both of Urshifu's dual STAB and fires back with Spore and Giga Drain.
Tangrowth has much higher defense, so it can make up for not resisting the fighting STAB. Basically does the same thing as Amoonguss with Sleep Powder and Giga Drain. It also gets Regenerator like Amoonguss.
Hope this helped!