Ap Assassin Item's Idea's
Hextech FBB-1
Basically it's an item that's just a belt of flash grenades with the following.
+80 AP +5% Movement Speed
Builds From: Hextech Revolver+Blasting Wand
Active: Flash Bang 3 Charges(refillable upon back) 40 Second cooldown.
Throw a flash grenade in an arc, the flash bang detonates upon contact with an enemy champion. A champion hit by a flash grenade becomes blinded for 1 second.
Cost: 2500
Notes: No one likes to not be able to kill their target because they keep kiting back while dealing 1300 damage in auto attacks. Some would say Zhonya's fix's this issue, well it doesn't, while in zhonya's you can't move, all the enemy has to do is wait for you to come back and kill you then. It would be nice for AP assassin's to have a very short window of time where the adc can't auto attack them and burst them down, and believe me, it does happen. In addition this item would be more Niche, but a much needed one, in games where a carry get's way to far ahead an assassin is left pretty useless because the ADC can simply kill them. This item helps with that by giving a small window of time where the ADC's auto attacks just can't hit them, it will likely only block one auto attack each flash bang but that's the point, if it were longer the ADC wouldn't be able to do anything at all.
Edit: In addition, AD assassins can get pretty tanky, they can build several tanky items, AP assassins can't and shouldn't be able to, they scale better late game so it's only natural that they have an item that not only helps against ADC's who reach late game but also let's them take less damage without being tanky.
DeathfIre Grasp(The Return)
+85 AP +200 HP
Build Path: Needlessly Large Rod, Amplifying Tome, Ruby Crystal. Cooldown: 90 Seconds
Active: Deals 15% Maximum health magic damage over 2 seconds to a targeted enemy(5% if ranged) and applies Doomed to them. Passive: Gain 5% bonus movement speed when moving towards enemies afflicted with "Doomed"
Doomed: Enemies afflicted with doomed take 10% more magic damage from the champion who inflicted it(5% if ranged).
Cost: 3100
Note's: Assassins like movement speed, the only item that's for AP's that gives movement speed is "Lich Bane". I always felt like Deathfire Grasp was simply not made correctly causing it to be completely broken, if it did the damage over time, it gives time for the target to heal. In addition, champions like Ahri can't abuse it like they did before because it doesn't work NEAR as well for ranged champions.
Bonus: There are a lot of items that i think would be pretty cool to have, though some less than other's. Like a Smoke Bomb that turns the user invisible for a very short time or make an area around the person that you have to step in in order to see them(the opposite of Graves smoke bomb), the issue is it would probably end up broken if not melee only and who knows who else could abuse an item like that, some champion aren't balanced around having invisibility(even if it would be cool).
These are the only two items i really think would be nice for AP assassins, it gives them what they need without being the exact same as AD Assassin itemization, keeping them seperate entities with different niche's they can fill, with help from these items.
Edit: Hextech FBB-1 could deal damage but i didn't want to overload an item. In hind sight it could also not be a hextech item because then it would be useless for some champions that want Protobelt or Gunblade instead.