I think the most obvious have been covered, but I think for this I'm going to try and stay away from the far too easy to choose from, Shadow Isles champions.
Death, Famine, War, and Conquest, let's see...
Well starting with Conquest, I'd have to go with:

The idea of Conquest was an archer essentially, or someone carrying a bow, wearing a crown. Sound like anyone we know? She is the queen by sort of a false "victory". Think her archetype and backstory fit this well.
War I think fits closely with Ashe funny enough with the champion I would pick. The idea here is surrounding the color red, someone more fiery in nature, and specifically possessing a great sword (as in a great sword, not describing it as "great").
My choice for War would easy be:

This one is hard, because the whole idea of famine with the biblical reference has to do with either raising the prices of food to a ridiculous degree so no one could afford it (hence carrying the scales) or lowering the amount of food to a literal famine degree.
This one was a bit trickier, but for the horseman of Famine, I would have to go with:

He is the closest to someone who would bargain to essentially jack up prices (with the scale symbolism of using the scales in the market sense, not so much the judicial sense), as well as almost having a gluttony feel to him, so maybe even his hunger causing famine of sorts. Plus...he is effing creepy.
Death can be obvious if we go with the shadow Isles, but barring that, I think this could be pretty easy to just give to Kindred. The character is pretty much the representation of death in the League of Legends lore, and it fits the literal interpretation quite well I think. Death in the biblical sense didn't carry a scythe as much as they were followed by a creature that would consume the victims death had slain. This could be lamb slaying and wolf being the follower.
So for Death, the easy answer (despite the lengthy expalantion) would be:

So tl:dr
Death:
Famine:
War:
Conquest/Pestilence: 