We need actual diver items
I've been trying to make builds for my favorite divers, and for years I have found that nobody has less satisfying itemization than an aa-based diver. I probably created 50 different builds for Nocturne when I mained him, and eventually abandoned the champion because no build I ever made was satisfying. Either you use the oneshot build which works well but doesn't make for interesting gameplay, or you go for a dps build and can't always keep up with mobile champs. Now I'm doing the same thing with Warwick. Fun champions are losing their appeal because of their unhealthy builds.
About their builds. What's wrong with them? Look at your current diver builds. Let me guess what you have. Juggernaut items? Assassin items? ADC items? I'll bet that you have some really odd mix of items that overall work out, but does not work as smoothly as builds for any other class.
I think it's best to look at what items are often picked up by divers, and take a look at what they need to be specifically tuned for divers.
1:
Great tank/juggernaut item. Works well on some divers, but for those trying to weave a bit of burst into their attack speed builds, this falls flat. I think both sheen and phage could be components for two separate items geared toward divers. Sheen for divers that stagger their damage with delayed combos (like camille) and phage for the more basic auto-based divers.
2:
Remember old youmuu's? Was really nice with the conditional attack speed. I doubt we need another dirk item, but I'll keep the active in mind.
3:
Its instant cc removal is nice, but sometimes divers would rather not sit on the key just waiting to be cc'd first. They sometimes need a type of cc removal more like cleanse.
4:
There aren't many great lifesteal options for divers, and those that do add to their sustain are not really meant for them. Tiamat currently builds into two high burst items geared for assassins or tanks, but divers often build them. How about a better dps option?
That should be enough. Here's the new items, based on the items above.
1: Mercy's blade. Builds from

low ad, medium health, high attack speed, phage passive (cleaver style), Unique Passive: Damaging a champion with a single target spell or attack grants you ad equal to 3% of their missing health. Expires after 3 seconds, recalculates when you switch targets.
This is meant for those divers who want to clean up better, but lack high burst. They can easily finish off low enemies with dps, provided they have the tools to reach them first.
2: Sword of Lead. Builds from 
medium mana, medium ad, 20% cdr. Passive: after casting an ability, your next attack causes the target to bleed for 30% of your ad per second over 2 seconds. Basic attacks increase the duration by 1, to a maximum of 5 seconds. 1.5 second cooldown, bleed does not stack.
Great for champs that use an ability to reach their target, and rewards them for sticking to them afterwards. Increases dps, but encourages you to itemize for damage.
3: Berserker's Gauntlets: Builds from
very high ad. Active: Silences you for 4 seconds, but grants you 100% attack speed and 20% movement speed for the duration. 60 sec cd.
This item is for the bold. It has a nightmarish build path and does not do much to help clear times, but on a champion willing to forgo spells for a few moments, they gain very high damage potential. For the most part these will be relatively tanky champions that are already in the midst of the fight and want to take out a carry.
4: Battleworn Flag: Builds from
medium armor and mr, raptor cloak passive, Unique Active: Grants you a 100% movement speed decaying over 3 seconds, and 0% tenacity, increasing to 90% over 3 seconds. 60 second cooldown.
This is another defensive option for divers that find themselves in teams that can't seem to reach the carries. They would likely swap this with GA in their builds, sacrificing a little safety for a better chance at the carries. It also replaces the reactive cc cleanse of qss with a more proactive effect.
5: Pillager's wrath: Builds from
medium ad, medium attack speed. Passive: Every third auto deals full damage to all nearby enemies and applies on-hit effects to each. Active: Your next 3 autos all deal full damage to all nearby enemies. 30 sec cooldown.
This is good for on-hit champions who always have enough single target damage, but want enemies to be more afraid to just group up on them. Also good for clear.
