He has about as many attacks as a single Blood Knight. Picture him as that. Sure tough to kill, but he doesn't wrack up enough CR to make him worth his while. Worry about the unit he's with; his 4 attacks will eat any of your units, so it doesn't really matter what you use. Skeletons will have a ward save however. If you kill his unit, you kill him. The points he puts into Tyrion for 4 attacks, you can put into a Vampire Lord with 6 or 7 attacks with Red Fury. Tyrion is NOT scary. He will contribute 3-4 CR a round. You can easily build a lord that will contribute 6 or 7 CR. Yes, your lord cannot engage Tyrion himself safely. But that's what using a champion is for. Just don't get into base to base contact with Tyrion with your Lord, and eat his unit. Tyrion, by Himself, cannot beat a unit of zombies. He just can't deal out enough attacks.
What he can do is demolish your elite units. Any rare choice will fall easily to him.
If Tyrion is in a unit like this, then match your lord up like this (E is elf, T is Tyrion, G is ghouls or graveguard, whatever, V is vampire lord).
EEEEE
ETEEE
GGGGV
GGGGG
If your unit charges his, don't challenge. If Tyrion Challenges, accept with a champion. Your champion will move into contact with Tyrion. From then on, I don't think Tyrion can slide around in the front to get into contact with your vampire lord. If you can VHD into combat, it should be doable. Don't attack Tyrion at all, just attack his unit with your unit and your lord. If you have a tooled up combat lord, you will win combat, and slice his unit down turn by turn. In 2 or 3 rounds of combat, Tyrion will not be able to win combat and will break.
True, Tyrion is mounted and has a M of 10. No problem. He only really gets to use that M score if he's on his own. In a unit, he's slowed to it's speed. If he wants to go outside his unit... well be my guest. If he does that, I would just try to dual charge him with something with a high M (Dire Wolves) and an Infantry Block. If the infantry hits him and can isolate him, he'll be running in no time. The only unit he can really be in and use his high M is Fast Cav; if so, Gaze them. If he's with heavier cav, he's not as mobile as you think.
I must stress to you, do not try to kill Tyrion. Just kill the units.
Oh, and another option would be just having a Wight King with the DragonBane Gem and Sword of Kings. You'll have a 2+ WS against all his attacks, and Killing Blow is his weakness. And that kind of Wight King isn't very tailored.