Sunfire is fine on Karthus but only a certain KIND of Karthus.
I generally put Karthus's setup into two categories. The first is alternatively called "Suicide Karthus" and "Zombie Karthus". Zombie Karthus is all about getting those damage numbers as high as possible and counting on his passive to let him do major damage in a teamfight followed by a colossal ult.
The second I call 'E' Karthus. This build is, kind of obviously, centered around staying alive and maximizing his short range AoE damage.
For Zombie Karthus I tend to like the following items:
Sorc Boots, Arch Angels, Deathcap, Void Staff, Hourglass, DFG. This gives you a truckload of AP and ensures that while you won't be dealing damage for very long, you'll be dealing a lot with it. The ult alone should hit for about 1k before MR.
Note that the theme with these items is that they are NOT limited by range (except for DFG's active) and thus help both his 'E' and his 'R'.
For 'E' Karthus you want to run something like this:
This one is a bit more situational. If the enemy team is only building small to moderate amounts of MR, you can grab the Sunfire for an extra AoE and some more survivability. If they have a lot of MR, then the Voidstaff comes into play. You can get away with waiting until you see quite a bit of MR on the field because of the penetration you're getting from boots, Liandry's and Abyssal, which adds up to a nice amount.
The GA is there if they're getting smart and focusing you down fast despite your Hourglass. In this case, you can hourglass, die and come back before even relying on your passive to let your E damage out.
Notice the theme with this build is to basically make Karthus live long enough that his 'E' becomes a long term DoT (followed by the DoT from Liandry's). Use his 'W' (the wall) to slow enemy's and trigger the bonus damage from Liandry's as well.
This is a much more survivable Karthus, but you WILL do less damage unless you have prolonged team fights where you don't die fast. Despite this not being Zombie Karthus, however, you should die fairly quickly from being right in the center of the action.
Those are the two builds I know of, obviously if you poke around guides you'll find even more.