Greetings,
I know a team that worked for a large IT firm and had its own 'Naa-Real' award. This was a session to dig in and make a pun on almost every incident that happened during the quarter. Right from failing deadlines with the 'Men at Work - Award' to personal failures like 'Damage your own career - Award'. A few more were 'Never been friendly-award', 'No one should talk to me like that - Award', and so on. The idea was very weird but worked well as the team had a good understanding with each other and took it in good humor. The prizes were real coconuts, given away as trophies!
This may not work if your canvas is bigger. However, please think of the brighter side of every tough situation and acknowledge the strength taken ahead from it. A fun award would serve its purpose if it can make them smile even years after they have received it. :)
Wish you all the best!