Use this guy 
I never see him be played but I randomly got him from a reroll. I slayed a Riven and she had to have ganks constantly lol. Jayce is like a Jax and Lucian combined. He is awesome but won't do so well against an Ahri or Yasuo.
Jayce also hard counters Tahm, Jax, Win Nhao, Nasus, Darius, and a lot of other meta tops. He's not the easiest champ though, so he's not popular.
he isn't a bad pick, but against a riven its really not the best. She's going to level 2 power spike, freeze the lane, and force you to use mana to farm from a distance which she can deny with her E. He can try and poke all he wants, but the more that progresses the more she can outgrow in farm, if you try to go up she will deny you that farm.
If you can bait her over and then knock her into the tower you will have a decent chance of winning.
Of course that goes all down the tube if she builds a blood thirster and not a hydra cause she will just gain a shield and life steal any harass you give, well farming well your working on the manamune.
Also consider that flash can go over projectiles like ashe arrow and jayce's energy bolt which can deny a good amount of damage in a all in attack against him.
