I think almost all of the currencies are considered annoying to all, but there might be some still fun out there. My list:
Timewarped Badges: Fun if you like the current timewalking expansion rotation;
Trader’s Tender: It’s a chill grind and not much time-consuming, and there is a 30 day window
Bronze (Mists of Pandaria Remix): I like this was abundant everywhere so you had a lot of liberty to choose the grind by quests, killing mobs, dungeons/raids etc
Gold: one of the few currencies to never lose its value. Talking about in-game farming of course, not credit card swiping (tokens). Depends on the playstyle, and how much gold you want, but I find it fun sometimes.
Honorable mention: PVP honor (no pun intended!): Could be fun if you like PVP of course, and providing you win most of matches
I loved doing the remix bronze. You could get it just by flying around! I would fly around picking up bronze while I waited for my queues to pop.
I enjoy collecting tender as well, mostly because looking at the list of activities gives me ideas for what I want to do that day.
“Grinding” anything isn’t all that fun, to be honest, but if it just comes with the game play, it’s okay. Oh, and I loved pissing on opposite faction bonfires for whatever currency you get with that holiday.
Bronze from MOP, that was really fun after you became super overpowered, then I hit max allowed and then the sparkles annoyed me.
Timewarped Badges I’ve always tried to collect as many as possible for if new rewards appeared, it paid off, not all new rewards are to my liking but if I want them, I have plenty of currency.
I loved grinding emblems in Wrath and Valor in Cata in random heroics, because they gave a piece of now 626 ilvl equivalent gear every 2-4 weeks, except weapons and trinkets, I think. It was a fun casual grind without much effort.