Ravager was kinda onto something with the necromancy mentionings, in my opinion. Check the Telvanni: they live for long periods of time through dabbles in necromancy.
Though with that said, you'd have to have the guy be incredibly competent in magic.
There was an Orc Necromancer, Magister Ulliceta gra-Kogg of Orsinium, high in the Mages Guild in the Oblivion Lore:
http://www.uesp.net/wiki/Oblivion:The_Black_Arts_On_Trial
So it seems highly probable that Orcs can become powerful mages perhaps to the extent they learn to extend their lives.
It's also mentioned that many believe that Hassildor uses sorcery to prolong his life. I know he's not REALLY a sorceror and his longevity is a result of vampirism but everyone seems to accept the sorcery explanation. If Imperials are believed to be able to extend their lives much like Elves do, then Orcs should be able to as well, albeit to a lesser extent.
A nice touch for a long lived "paladin" would be to have him bound to an enchanted, Umbra-like weapon of some sort, which steals life from those fallen by his hands and gives it to him.
That could have been part of a deal with some Daedra or another.
If he follows a Daedra Lord, he'd be less a Paladin in the "Lawful Good" archetype...more like a Death Knight or a Black Knight. (I know I'm seeing things in a simplistic black and white point of view but considering Orcs would likely follow the likes of Malacath, their code of conduct wouldn't be very Paladin-like)
On the other hand, perhaps an Orc who was blessed by Talos or another Aedra and wore armor enchanted by priests of his order would fit the Paladin mold a bit more. With certain enchanted items or with the blessings of his patron deity he could live a long time.