The side-quest was indeed in D/P/PL as a daily quest done thanks to the internal clock of the NDS.
Your idea is similar, but with a different prize in mind (money) while the D/P/PL rewarded you with a special type of Pokeball. I still support this, because extra cash/stones/braces would be great to get daily for sure, rather than praying RNG gives you a certain pickup item, or paying high-dollar for breeding items.
Regarding to random Pokemon selection, have it be any obtainable 'mon and you go catch it wherever it normally appears, instead of an extra area.
Only problem is that PokeMMO handles days differently from the handhelds (multiple in-game days in one irl day)