Greetings,
I know a team that worked for a large IT firm, had its own 'Naa-Real' award. This was a session to dig in and take a pun on almost every incident, that happened during the quarter. Right from failing deadlines with 'Men at Work - Award' to personal failures 'Damage your own career - Award'. 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 as the team had a very 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 out the brighter side of every tough situation and acknowledge the strength taken ahead from it .
A fun award would serve it purpose if it can make them smile even years after they have received it :)
Wish you all the best !