Personally, when Death Knights came out some of their talent trees were exactly same of a paladin's but in a darker nature. I always thought of a Death Knight has the polar opposite of a Paladin. Where the Paladin wields power from a holy nature and Death Knight wields it from an unholy nature. I think it would be as simple as changing the Unholy tree into healing tree and it basically comes down to the belief that they would be reanimating their target, nothing holy about. I played Unholy for a long time so I'm not going to just say screw all DPS Unholy but the concept would easily work.
Would add a layer of uniqueness for sure, every healer in the game deals in nature or in holy powers. A healer that heals from an unholy power that just sends sinister and cool.