3 move units can start outside of explosion range, then hit and run back outside of explosion and counter attack range. Horse units, or recon units with mobility, or other units with both mobility and haste. Pyre Zombies may mitigate this by putting defensive terrain like forests and hills between them and your stack.
2 move units can start outside of explosion range, then hit, and end move inside explosion range of all the rest of the kills caused in the turn and counter attack range. If you have strength in numbers this works but is costly. Normal recon units, or most units with the mobility promotion fall into this category.
1 move units don't work without access to healing in between attacks. Kills they cause will cause damage to their entire stack, bringing them to critical levels of health after a few victories. They will end turn in counter attack range. Don't get into this sort of fight if you can possibly help it.
Units with access to healing can just about work. I'm specifically thinking of wood golems, with heavy enchantment adept support. The adepts stay behind the golems, and move in one by one to heal(and with haste or mobility, retreat outside explosion range again). Despite being vulnerable to fire an empowered wood golem should be decently superior in a one on one fight to a pyre zombie. As long as the adepts can keep them healed, the Wood Golems can win. The golem player needs many more hammers worth of troops though.
Mages with Destroy Undead absolutely devastate Pyre Zombies. Elohim devouts can similarly be upgraded to priests with Life 2, making them an effeective counter.
Summoner mages can work. But both fireballs and spectres are very very poor against the zombies, which rules out most summoners. Ice, Law or Entropy summons will still work well however, and if the mage has either mobility, has been hasted or has spell extension then the mage will work as well as a three move unit. It's almost always better to go for the life mages though, unless you really can't get access to life mana.
Mage based options all require many more technologies than the Pyre Zombies so won't stop an early rush.