1) Could host a treasure hunt... But it will take a lot of planning... Give some clues for every checkpoint a player reaches.. 4 regions should be more than enough to host a hunt.. the final destination could be an NPC, or any random thing (you could use riddles here too, to describe the checkpoint/destination). Since we won't have support of PokeMMO devs/staff to help us here.. a host should manually give the clue whenever a player reaches a checkpoint.. (this could be done with 2-3 player groups too if there are enough members) btw 4-5 of the hosts can hide as checkpoints too and give a DM about the next clue for the next host checkpoint..
2)a catching event where a description/riddle of a Pokemon could be given and players would run to hunt and submit (transfer) that mon to a host for confirmation..
3) A PokeMMO nuzlocke could be good too.. adding stricter rules, player reaching furthest wins, or in a time constraint the player who gets 4 badges first would win.. no outside assistance from players/alts/GTL.. using a new character ofc (adding strict nuzlocke rules ofc, but monitoring every player could be a problem)
4) A PvP event could be done where a host will select the 12 Pokemon to be used (sweepers/HO only please and no hazards/removal, it will take too long).. and ask the 2 competitors to pick 1 of the 2 Pokemon (don't reveal the Pokemon and give them in sets of 2 each, one player gets to pick first one turn and the other gets to pick next turn) basically a draft league.. (this could be done better in Showdown imo)
5) GTL flipping challenge... Well this could be decent.. the ones who make the most profit within a time schedule (maybe 1hr) would win (after calling GTL fee obv).. The mons should sell within the time given btw.. there will always be a record of purchases/sales in the GTL.. no selling personal mons and buying your own mons listed.. (wish we had a feature to record who purchased whose mon in the GTL)..
6) NO STAB Tournament: An OU tournament with Mons that have no STAB moves in its Moveset could be decent imo.. by no stab I also would add no defog for flying types, no Stealth Rock for rock types, no Spikes for ground types, no taunt for dark types, No Calm Mind for psychic types and also No Recover/Softboiled for normal types, No roost for flying types.. etc; (Showdown can be a great platform for this).. I can already see Tyranitar being abused
These are off the top of my head, I haven't thought much.. neither thought much about how to regulate these.. just suggestions
There are also many more like gym rerun challenge, Monotype challenge (but actually Mono type, single typed mons) etc;