Offensively WoW HexPult and BU Zeraora do decently against it, along with common scarfers like Togekiss and Hydreigon. Unaware Quagsire is also a decent check. Unless they HJK on the switch (hard to do with ghost meta) Quag isn't 2HKO'd by anything.
In terms of more experimental stuff there's a lot of bulky grounds that you could mess around with. Runegrigus is something that comes to mind as a fun counter with that HJK immunity and Pyro resistance. Torkoal and Golisopod are both niche mons that do well against all of its commonly run moves, but they struggle long term due to a lack of recovery. This paragraph is completely theorymonning but due to the newness of Cinderace the meta hasn't had time to adjust to its presence yet.
With Libero out now, I don't believe Dragapult can be considered an offensive check any longer, sadly. Pseudo-STAB Sucker Punch has a chance to OHKO after Rocks.
252 Atk Libero Cinderace Sucker Punch vs. 0 HP / 0 Def Dragapult: 270-318 (85.1 - 100.3%) -- 6.3% chance to OHKO
The one way I could think of Dragapult still combating it is if you predict the Sucker Punch and WoW in response, since I believe Cinderace will become Dark-type even if the Sucker fails. Someone correct me if I'm wrong on that. I also don't recall if becoming Fire-type again through either switching out or using Pyro will keep it burnt, or if it will heal that when it's Fire again.
Additionally, Runerigus does not actually resist Pyro Ball. It still has massive bulk and only takes 31.8 - 37.5% when fully invested in Defense, but Pyro Ball is neutral on both Ground and Ghost. Libero Sucker Punch actually does more damage to Rune (36.2 - 43.7%), but could be interfered with by Wandering Spirit. With clutch switches, you can lock it into an undesired type and either hit back (if it's still Fire), or use that time to set hazards or even burn it (if Dark/other).