Balloons

Yes, friends have been getting them rather regularly from shadow missions with mobs that are higher than their CP, and some mass killing boss rated CP mobs are getting even more.

I have been rather busy in RL so I've been mostly AFK fishing in Doki Doki and have yet to fish up a single deflated balloon (R3 fishing). So I think its safe to say you don't get them there.

Also you must turn in at least 1 inflated balloon to get the prize when the 'hot time' comes up. This means if you have multiple alts you can turn in 1 inflated balloon for a club then switch back to your main and after the 'hot time' passes you can log into your alts and collect Consolation boxes.