How is she viable as a support?
Irelia has a kit that can lock down a certain champion. Her e can stun an oppoent when her hp percentage is lower than the target's. As a melee support, Irelia will definitely be taking some harrass from the enemy ADC, so she most likely will have less hp percentage than their ADC, guarenteeing a stun when an all in is initiated by either sides/ganked and need to escape. Her e is extremely useful in different situations and at times can allow outplays to happen when e is maxed with its 2 second stun duration. After laning phase, you will become the true protector of you ADC as your utility will come to great use. With full CDR, her e CD is pretty short, allowing it to be used multiple times during an average teamfights. This allows you to maximise your effect in fights as you can land stuns on targets that threaten your team or adc the most.

She also has great gap closer, with her q resets. This provides you with mobility and higher chance of landing stun than e.g. taric's on enemy adc. Your passive (tenacity that scales with number of enemies) also ensures that you can be active in fights longer and do as much as possible for the team.

Pros:
>reliable stun with short cd into mid game
>protect and peel for ADC (even better with passives of items)
>Lock down enemy threats
>help ADC melt down tanks with Hiten Strike(W)
>Gap closer

Cons:
>Squishy early game,gets harassed a lot and cant do too much in lane other than warding and landing stuns in all-ins
>Item reliant, really need the tankiness and item passives to be effective
>Stuns can be hard to land if not familiar with how it works
>Might be blamed for losing

Frozen Heart and Zeke's Harbinger on top of the new support item Eye of the Equinox are essential for Irelia. Together, they provide you with 40% cdr, tankiness and more importantly, frozen heart passive can shut down enemy adc/assassin, while zeke's harbinger empowers you and your adc, because it synergises well with the new mastery (gives bonus critical chance for a few seconds)

If you need another armour item, consider Randuin's Omen because of the extra cc it provides, crucial for a support.

For magic resist, consider Locket of the Iron Solari over Spirit Visage even though it provides you with less mr, because that way benefits the team the most.
if you desperately need more cc or sheen passive, then consider Iceborn Gauntlet, or if your adc needs you to help kite e.g. nasus, go for Frozen Mallet for the slows on your aa.

Laning is the toughest phase for Irelia support. Communicate with you ADC, make sure he/she doesn't play aggressively and to just focus on farming. Try to only go in when your ADC has item advantage, or when your jungler comes to gank. Take some harrass occasionally so you can guarentee to have lower hp percentage than the enemy adc, the best way to do that is to kill canon creeps to share gold with your adc, as your lane will be pushed most of the time, you will more often take harrass by walking up to the canon creep.

After surviving laning phase, you most likely have a sightstone, boots and upgraded gold income item. You are still not ready for fights. However, as dragon fights are very important at this stage, play passively in fights and ALWAYS stick with your ADC, save stuns for important targets as your CD on e isn't short yet at this stage. Make sure you ADC survives, and then when your team is winning the fight, don't hesitate to q onto squishy enemy targets, and burst down as much of their hp as possibly with your full combo (w>q>r,r,r,r and aa s). Remember, ONLY go in like that when your team has significant advantage in the fight, or it is highly risky as you won't be doing much damage with Support irelia build.

After Dragon fights, stay in lane for as long as possible after warding important areas. Kill creeps to share gold with your teammates whenever you can. Therefore you have one objective: GET RICH. Pay attention to the map and make sure you stick with your ADC when a fight is coming up. REcall at the right times to get your items. When you have your cores completed, you are ready for fights as you are tanky enough and you can provide enough utility for the team. That should be around the 25-30 minute mark in an even game. After that, you have ONE goal: PROTECT and PEEL. Make sure your adc survives teamfights by locking down enemy threats with your stun. Don't dive in without your team being in significant advantage. If you can do this, ward well and control objectives, I believe Irelia Support can be pretty viable and effective.