Random Ideas for Items (geared towards AP Assassins)
Note that most of these items either have actives/passives that don't benefit mages very much or have actives/passives that are nerfed for ranged champions (mostly mages). All these items give AP Assassins more options, similar to AD Assassins, without allowing mages to abuse the items because they are mostly geared towards melee and single target attacks whereas Mages have a lot of AoE and are far ranged.
Most of the items provide movement speed which is what mages don't really need and provide no mana which is a stat that mages really like so using an item slot on these items would hurt their mana pools if they decide to go for these first over a mana item. In addition, none of the items provide CDR which is another stat mages like to have.
Although Book of Sorrow has stats that a Mage may like, the active requires them to be very close range which is something most of them want to stay away from. Divine Shadow's active is melee only and has a hefty price for an item that mages will only get half the use out of.
Aeon's Blade: Cost: 1250g (815g) Builds out of: Amplifying Tome -30 AP -4% Movement Speed -Unique Passive: +10 Magic Penetration
Divine Scepter: Cost: 2400g (715g) Builds out of: Amplifying Tome + Aeons Blade -60 AP -6% Movement Speed Unique Passive: +20 Magic Penetration Unique Passive: If an enemy champion is shielded (any type of shield), 50% of damage dealt to them will ignore the shield and do damage directly to their health bar (damage will ignore 25% of the shield for ranged champions)
Aether's Torment: Cost: 3000g (650g) Builds out of: Haunting Guise + Blasting Wand -275 Health -70 AP Unique Passive: +20 Magic Penetration Unique Passive: Each unique champion kill (not assist) permanently grants 10 out of comabt movement speed.
Book of Sorrow: Cost: 3700g (815g) Builds out of: Seeker's Armguard + Aeon's Blade + Amplifying Tome -80 AP -40 Armor -6% Movement Speed Unique Passive: +15 Magic Penetration Unique Active: Doing damage to an enemy champion that is within 200 range of you will heal you for 30% of the damage dealt (10% for AoE abilities) for 6 seconds.
Seal of the Ages: Cost: 2800g (1065g) Builds out of: Null Magic Mantel + Blasting Wand + Amplifying Tome -70 AP -45 Magic Resist Unique Passive: +20 out of combat movement speed Unique Active: For 6 seconds, single target spells and auto attacks against champions deal 20 - 100 (+20% AP)(+30% Bonus AD) magic damage over 3 seconds. This effect can refresh, but does not stack.
Divine Shadow: Cost: 3800g (1350g) Builds out of: Aeon's Blade + Seeker's Armguard -70 AP -45 Armor -8% Movement Speed -Unique Passive: +25 Magic Penetration -Unique Active (Melee Only): Channel for 1.5 seconds to grant a spell shield that blocks the next enemy ability. Lasts for 10 seconds.
Arkan's Tooth: Cost: 3100g (615g) Builds out of: Aeon's Blade + Amplifying Tome + Chain Vest -65 AP -45 Armor -Unique Passive: +15 Magic Penetration -Unique Passive: Upon taking physical damage that would reduce your health below 30%, gain a shield that blocks 150 + 1 per 5 AP physical damage for 4 seconds (2 seconds for ranged champions).
Bane of Affinity: Cost: 2700g (1000g) Builds out of: Aether Wisp + Blasting Wand -90 AP -8% Movement Speed Unique Passive: Using a mobility spell that damages an enemy champion grants the next single target spell or auto attack against them to deal an addition 50 (+10% AP)(+20% AD) true damage. Unique Active: Gain 30% Movement Speed for 6 seconds (3 seconds for ranged champions).

: We hereby expel ye from the AP assassin's union, thou hast dabbled in the dark arts of sustained DPS, AoE, range, reliable CC and utility. Thou art banished to the realm of mage. I'm especially ashamed of you Ahri, I undestand you were shaken by the loss of your best friend, but you have gone too far.