I dont know about my ability to come up w a new game, but I can tie it into the games u already have...

U could tie it into the daily trivia game, who wins day by day... best hand at the end of the month

or tie it into the football pickem... assign each game a card, if U pick the game right, U get that Card... (maybe assign a flop to the team on thursday game, a turn to each on the sunday night game, and a river to the monday night game?)... and if u do it this way-
I was try to tie betting into it like, start w 100 chips... but it doesnt really work w no hole cards and would just be every shoving after sunday...

u can do the connect celebity connection thing that way... assign the flop, then if u do it in 1 u get a Ace, 2 a King, 3 a Queen, etc... then one day deal a random turn, then a random river etc... I dont know how easy it would be for some one to control the amount they did it in, say like -get a straight in 3-5 straight days... or quads in 3-4 days