Melee ADC's do have some problems right now. I think the issue is largely a problem with itemization - melee adc's simply do not have the inherent defenses in their kits that ranged adc's do; namely the ability to attack at range. For melee adcs to properly function, they'd need to be able to gain defenses while still building offensive stats. On top of that, ranged adcs gain all of the same benefit from the items that melee adcs get from building the same items.
There are not items specifically talored to MADCS, and there are not enough items which are Melee Only in general.
There needs to be a melee only item, which gains defensive stats for building offenses, but Riot is really leery of building such things, because it would "benefit fighters." It's the reason why they don't buff Atma's for instance.
So... to have such an item, it would have to give some madc stats, with scaling defenses based off of those stats, be melee only, while paradoxically unscaling off of defensive stats.
Something like...
Jeden's Spiked Shield
25% crit chance
30% Attack speed
MELEE ONLY
Unique - Tenacity: The duration of stuns, slows, taunts, fears, silences, blinds, polymorphs, and immobilizes are reduced by 35%
Unique Passive -Jagged Spikes:
Grants bonus armor equal to your bonus attack speed. It loses 1 point of armor for each 2 points of bonus armor you have (outside of this item)
Unique Passive - Reflective Shield:
Grants bonus MR equal to 50% of your crit chance. Loses 1 point of MR for each 2 points of bonus MR you have (outside of this item)