I have never managed to get the ability to cast Destroy Undead in time to be important for dealing with Pyre Zombies. The Sheaim get Pyre Zombies long before I have Life II casters, and once I have Life II casters (assuming I survive that long) there is no need for Destroy Undead. Either the Sheaim have stagnated, or they have stopped making Pyre Zombies in favor of "more advanced" units.
The best way to deal with Pyre Zombies is proactive offense. Declare war on the Sheaim and crush them if you can, and if not then torch all their improvements and kill any attempt they make to expand. Limited to one city without improvements, the Sheaim won't get to Bronze Working soon enough to matter.
Of course, the Sheaim don't always start close enough for such a strategy to be practical. With the new AI economic improvements you might not even meet them (on a large enough map) until after they have Bronze Working. Sending some mounted units to pillage their improvements can put an economic hurt on them that makes supporting an offensive army impossible. If their Pyre Zombies never leave their borders, and only kill some Horsemen, then they're not really much of a problem.
If you do find yourself being invaded by a stack of Pyre Zombies then you've got problems. The new AI doesn't attack unless it is "sure" it can win, and it doesn't seem to take collateral damage from fallen PZs into account - meaning that even if they were just normal Axemen you'd be in trouble. Units in cities take less damage from Pyre Zombie explosions, based on the city defense modifier, but it really won't matter. 20 Pyre Zombies will kill 15 Longbowmen fortified in a legendary culture hill city, and you're very unlikely to have all of your cities so well defended this early in the game. Fire resistance will certainly help, but you may not be playing the Clan and earning enough xp to take the Magic Resistance promotion on all of your units is going to be impractical.
A better approach is to take the Mobility promotion on your melee units and employ hit-and-run tactics to pick off Pyre Zombies and then move away from the blast radius of future explosions. (You can also use Horsemen, although Copper Axemen are generally going to have better odds. If you don't have Copper, or you can't get to Bronze Working in time, then Horsemen promoted with Shock can do a respectable job.) Sacrifical Warriors can lead the enemy stack away from your cities, and into terrain that doesn't have a defense bonus (thus making your real attackers more successful). Just remember to send some Horsemen to pillage Sheaim improvements as soon as practical, because that is what will actually shift the tide of the war. The AI is so good at making units that you can crush wave after wave of attackers and the AI won't be bothered at all.