Ok before I start, I'm no expert with putting in exact number values to modify stats on a certain char. to make them more viable. these are just general suggestions that I think could help balance out some heroes.
Ryze - At the mo. I think ryze is pretty balanced and doesn't need much done to his new self.
Katarina - Haven't really had much in the way of problems with her...... maybe decrease the amount of bounces her dagger throw gets.
Cho'gath - Increase the aoe of his spikes....... its his only escape mechanic.
Nunu - All good, If you run into the whole enemy team and ulti expect to die =D.
Amumu - Maybe a bit more armor at the start, hes a bit squishy.
Veigar - Little bit more hp at the start, just seeing him getting rolled lately.
Singed - Make him cheaper, no one plays him anymore lol.
Tryndamere - Increase his damage growth for each lvl a bit more.
Dr. Mundo - Increase the cd. and lifecost of that **** annoying cleaver throw.
Gangplank - Im not sure if hes as powerful as he used to be but...... decrease his scaling with crit.
Malphite - Give him a bit of that armor back he lost a few patches ago.
Sivir - Still seems to be missing a certain something. maybe a slow coupled with her ulti...
Fiddlesticks - All good, awesome when played by someone good sucks if not.....
Kayle - Doesn't feel right, needs to be either a damage dealer or a tank not just suck at both....
Aniva - Never played her so can't comment.
Teemo - Pretty good, kinda feels like he needs a stun or something. like.... After 6 stacks of poison the target gets stunned for 1s (this effect cannot occur more than once every 10s).
Ashe - To much slowing, open to suggestions about her.
Annie - To squishy at the start, little more hp.
Tristianna - Over nerfed, give her back 25% of what she lost and see how she goes.
Jax - Don't see many ppl playing him atm so not sure.
Master Yi - When you kill a champ with highlander it refreshes all cd's except highlander, change his passive so it gives him chance on hit to deal 10/25/50 extra damge to minions. The 1st suggestion was from another member (feel free to take credit).
Corki - Haven't seen him since he got hit with the nerf bat so not sure.
Alistar - Reduce the mana cost on ground slam and headbut by 30%
Blitzcrank - Decrease the range on his rocket grab maybe, not sure.
Soraka - np.
Nasus - Haven't played him much lately so not sure.
Warwick - Maybe a DOT he applies when Blood scent is active or an attack speed boost.
Morgana - No real problem with her.
Rammus - Not sure, maybe a higher base health regen rate.
Kassadin - Maybe slightly better ap scaling with abilities at high lvls.
Sion - maybe make his enrage do a bit more damage to him, with the right partner I've seen sion's with over 1k hp at about lvl 4. pretty crazy.
Taric - Don't think theres any issues.
Janna - Decrease the range on howling gale, Instead of increasing the damage with physical damage from eye of the storm I reckon maybe it should regen hp.
Zilean - No idea, haven't seen him or played him lately.
Twisted fate - If their any good they can hit the stun card everytime...... bit of a long duration on the stun I reckon.
Evelynn - maybe instead of taking less damage from minions, she has a passive lifesteal similar to warwick.
Karthus - Increase the damge from Lay waste, increase the cd and increase the mana cost.
Twitch - Now for one I reckon if he gets to close to someone or a minion they should see him, something similar to the cast range of teemo's mushroom, decrease the damage from his poison but increase damage from expunge. Im rly not to sure other than that, what do ppl reckon?