This doesn't really have to do with Minecraft gameplay, but maybe a skin designing competition? Like, Halloween is coming up, so you could have a 'best costume' competition.
Or maybe first person to get all possible mobs in a bucket; cod, salmon, axolotl, pufferfish, and tadpole. Or if that's too easy maybe try to collect one of each tropical fish (there's 22 I think?). And then the next week's challenge can be to design the coolest aquarium for all the fish. Just make sure everyone knows that axolotls will kill everything so to keep them separate.
Some other ideas could be to...
>create an animal sculpture using as few blocks as possible.
>see who can put on the best firework show.
>see who can tame all 12 tamable mobs first.
>see who can become the biggest 'crazy cat person' (basically just taming as many cats as possible).
>do a scavenger hunt! Depending on your world layout you could create a scavenger hunt and put clues in books. First person to give you the right coords wins (X marks the spot!).
>have people come up with Minecraft puns or jokes and put them in books. The best or worst pun (depending on your opinion on puns lol) is the winner.
>see who can collect the most ominous banners
>see who can build the best 'zoo'. This could be really cool cause there's no limits to what kind of walls/fencing/barring they use, and it would be cool to see informational signs and the mini biomes they're in. But you could also not tell them that and see who gets the most creative. I'm a big animal (mostly reptile and crustacean lol) person so I'd be most interested in who builds adequate biomes and enclosures.
I hope some of these work for you! Or at the very least give you some new ideas of your own! :)
