First, verify that you indeed can't find Brynjolf. According to http://www.uesp.net/wiki/Skyrim:A_Chance_Arrangement:
When you come across a merchant named Brynjolf at the Riften bazaar
during the day or in the The Bee and Barb at night, he will propose
that you frame a vendor by planting a stolen ring on his person.
If you still can't find him, install the the Unofficial Skyrim Patch (mirror link) and see if it fixes this.
If not, try console commands to teleport Brynjolf to the player's current location:
I'd type these commands while at the Riften market area (where you're supposed to meet Brynjolf).
prid targets an entity - Brynjolf in this case. '20545' is Brynjolf 's RefID.
moveto player moves that targetted entity near the vicinity of the player.
Brynjolf should now be near you after doing this. If for some weird reason, he is dead (could be an effect of previous console commands tried, although unlikely as Brynjolf is 'essential'), use the console command
resurrect 1. Brynjolf should go back to life.
If for another weird reason, Brynjolf is still not near your vicinity after doing this, he may have been 'disabled' from the game (also could be an effect of previous console commands tried), making him not appear in the game. Type
enable in the console to remedy this. If he still isn't up, type
resurrect 1 again.
He should appear near you after typing in those commands. Try starting a conversation with him.
More info on console commands here: http://uesp.net/wiki/Skyrim:Console