Riven has a lot of power if she can get on top of you for free, if she needs to use 2-3 Q charges to gap close to you then her damage will be more reliant on her auto attacks, as Jayce you can swap to hammer form and hit her away as she tries to engage.
If you are looking for counter champions then Renekton can out sustain her and out trade her early, so you can shut her down in lane, Quinn can negate almost all of Rivens damage, just poke with autos and save E for when she tries to get on you, she can't really do much unless she flashes on top of you. Darius and Garen do well vs her but are always banned. Olaf is supposed to be pretty good vs her but I've heard this is still a skill match up. Shyvana can get to a point where Riven can't kill her quickly enough but she still deals heavy damage to Riven. Cho'Gath can shut down her combo with his scream, and gets too tanky to quickly kill, also he can out sustain Riven with his passive. Top lane Udyr can also work, since he can build somewhat defensive and still deal heavy damage in trades, also his W will help him negate damage and sustain.
There is also the option I pick in a lot of match ups on certain champions that scale really well, focus on farm, play back so they can't all in you and out scale her. I do this as Vlad, basically just AFK farm, and pretty much ignore the Riven unless she's trying to all in you, play way back if W is on cool down. I do the same thing on Katarina, get the farm that I can, wait for an opportunity to either 2v1 with the jungler, kill them if they are bad or roam to side lanes.