Pride:
I think Azir and Draven are the best contenders.Azir is extremely proud on his nation and really thinks he is the ultimate ruler,while Draven is simply Draaaaveen.
Though I'd say Azir is better fitting,since in Dravens case it is more that he wants attention.
Lust:
Ahri seems extremely fitting.Not only does she charm people,but she commited sins because she wanted to become human(and that desire can be interpreted as a form of lust).In Sorakas case,she wanted to help Warwick,so I wouldn't call that a sin of lust.
Shaco could also fit,since his desire to kill and hurt others is also a form of Lust(Lust doesn't just represent sexual lust,but also lust for other immaterial things like power or fun)
Going by the lust of power thing,I'd say Xerath would also be a good candidate.
Sloth
This one is kinda hard,because most champs aren't really lazy.Even Heimerdinger is inventing stuff and Urgot served Noxus for such a long time now that he doesn't even rest after his death.
Yorick seems fitting,since he regrets not making an heir or at least make himself a name in life.
Gluttony
Trundle and Nunu only bite/eat stuff as a fighting strategy and Bard isn't really fat,he just looks that way(and he also doesn't eat anything in the game).
Almost all the void champs could fit this theme(even vel'koz who basically consumes others to gather data about them),but I think the most fitting champion is the upcoming Tahm Kench,the guy is literally built around the concept of Gluttony.
Wrath
Tryndamere is the ultimate wrath champion.No other champion is so focused on his/her wrath like Tryndamere.
Sure aatrox is often associated with wrath,but he is actually more focused on inflicting blood lust in others.Brand could also fit this,but he sees what he is doing as something that needs to be done,he isn't necessarily driven by rage.
Envy
I'd actually say Zed is the best champion to represent Envy.
Think about it,Zed just wanted to be aknowledged by his father,but he was always overshadowed by Shen.So he learned the forbidden techniques just to get the same recognition that Shen got,but got expelled for that.Him overtaking the kinkou was most likely a way to prove his father that his teachings are superior,he still wanted to get the recognition that shen got.
Greed
I think Kalistas desire for revenge would fall more into the category of wrath(since she wants to do it out of anger) or lust(its not like she really gains anything from it).
Sivir is quite fitting as she really just cares for the money.Swain could also count,since he has overtaken one of the biggest city states in runeterra and he is seemingly bent on expanding his territory(but in the end his motivations are still unknown,so we can't say for sure)