I used to give it to whoever impressed me in the run. However, it's very hard for a DPS to be impressive. We don't have much we can do that stands out other than making sure we don't pull agro, which could always be a fault of the tank rather than a fault of the DPS. We don't prevent wipes like Tanks and Healers do, nor do we do anything but speed up the majority of runs that a Warrior and a single healer could probably manage on their own.
In the end I decided to give it to whoever was nicest in the run. If someone explains something in a dungeon and doesn't act like an ass to the new guy they automatically sign up for a commendation. If someone says hi at the start they also sign up. If they tell someone they're doing something wrong in a nice way they automatically sign up again. Whoever gets the most "sign ups" gets it.
If the first thing they say is "SR?", though, they automatically get no commendations no matter what miracles they pull off in the dungeon. I'll give it to the other DPS (if they aren't the "SR asshat") if no one deserves it because I know we rarely get them.
However, I'm very likely to give Bards a commendation if they're good. We had a Bard save our group in Ifrit HM today with a very well timed LB3 when both healers died from plumes. Mage's Ballad is another good move to get yourself commendations.