My player likes the Subclass you drew up:
So I think this is pretty easy to do with some modification of the Oathbreaker subclass, with the following additons/changes:
3rd level: creature type changes to Undead, immune to poison and necrotic damage as well as poisoned and frightened conditions.
Subclass spells: Command, Compelled Duel, Hold Person, Magic Weapon, Dispel Magic, Elemental Weapon, Banishment, Staggering Smite.
Replace Dreadful Aspect with a Channel Divinity that gives Magic Resistance for 1 minute as a Bonus action.
7th level: Eliminate Fiends from the Aura of Hate feature but add that all undead, including the Death Knight have advantage against saves from being turned
15th level: The Death Knight can use an action to hurl a ball of fire 10d6 damage, dex save for half. The Death Knight can do this a number of times per day equal to half their proficiency bonus (rounded down).
20th level: On being hit by an attack the death knight can use a reaction to give himself a +6 bonus to AC. The bonus lasts to the start of his next turn.