What AP based champion can do the most damage in two seconds? not counting nunu or shaco.

Taking into account that Veigar and Thresh have no AP limitation, those two champions would deal the most Burst, however usually you won't get enough AP on Thresh to compete with other AP burst champions.

Veigar however would be the champion with the highest single target burst in a realistic scenario. His skills and Items:

Q: 260 + 60%  AP
W: 320 + 100% AP
R: 500 + 120% AP + 80% enemy AP
Deathfire Grasp: 20% of Target Health and + 20% magic damage increase
Lichbane: 75% Base AD + 50% AP (75% Base AD of veigar on lvl 18 = 71.625)
Arcane Blade: 5% AP

Can hit in under 2 seconds. It is very possible to gain 1000 AP in a game with veigar with a normal build but I wouldn't recommend buying Lichbane a lot but I'll include it here for the highest possible burst damage in under 2 seconds.

Now If you open up with DFG you'll already have 20% of the enemies HP and a 20% magic damage increase.

This means you can hit for a total of: 20% HP + 1381.95 + 392% AP + 96% Enemy AP with DFG, Your Skills and an autoattack.

Let's say you're up against a Syndra on level 18 with 2000 HP, 600 AP and 100 Magic resistance while you have farmed up to get exactly 1000 AP.

If you full Combo Her you'd hit her for:

400 (20% HP) +
3920 (392 % of your AP) +
576 (96% of her AP) +
1382 (Base damage rounded up)
_______________________________
6278 Raw damage

Now even if you take her Magic resistance into account you'll still deal 3139 damage which is pretty much an overkill. So this is one of the more realistic burst scenarios but of course it differs from situation to situation.

In the end most champions that are designed to burst someone down have a huge damage potential and are good at their role. You could take champions like Annie, Leblanc and even a Cho Gath can deal a huge amount of burst damage if played full AP. But Veigar has the highest amount of burst within 2 seconds in a realistic scenario.