I could understand there being rewards, but they would need to be tailored for long time tribunal workers. This would kind of work like a season in LoL ending, and people getting a skin for their efforts over the year.
The trick is, how does Riot reward people who put in a lot of work, while not neglecting people who are new to the process and don't fall within a certain guideline for the reward system. There would need to be a combination of things, such as justice rating, case accuracy, number of cases solved, and time spent doing cases ( this one is tricky)..
And even after all this, the rewards would have to be something which again, wouldn't alienate other players, Tribunal workers, or future Tribunal workers.
People say that the system is built around using people who do the work simply because it's the right thing to do, and, I think for those people, that there being no reward, isn't an issue.
Me personally, I don't care about a reward. The reward would inevitably be something that I don't need or wouldn't use more than a few times. So, why ask Riot to go to those lengths, and, why not simply work to make the community a better place.
There will always be people willing to do the work 'just because it's the right thing to do'.
EDIT: I voted maybe. Because I could see the system going either way, as a positive or negative attribute to the Tribunal. But, more over, I think it'd be very hard to balance, but, if anyone could create an unbiased and uncorruptable reward system it'd probably be Lyte, and the people that work with him/her.