2009 R6S Idle and Running issue

Do a lot of sitting? Hopefully there's not a bunch of crud in the injectors.

Test the ignition coils. There's a downloadable PDF manual. It will tell you how to get into diagnostic mode where you can fire each plug individually. Remove coil, connect to spark gap tester, wrap coil in grounded foil and test for spark. Note the gap at which point spark becomes less than 100% reliable. Compare each coil. The coil that quits firing reliably at a fraction of the gap of the others is bad. The coils typically fail within a year of each other so may as well replace all. Replacing coils for the 2nd-Gen bikes is another can of worms since the newer coils all have higher resistances. Far more frequent re-gap intervals are required unless other changes are made. It's also not unusual for people to get bad new coils or new coils that don't last long due to poor insulation and leaking spark to the cylinder head.