I have some pets in mind that I really wanna use, and they're just sitting there in my stables, but i'm not sure how to level them up to 60 so fast. Gaining levels is so slow and I need a faster way.

Well...


Use a leveling service in igroups and guilds. Kinda slow tho if the person isn't on or has other pets to do. And forget festtime.

Set them to one proficiency, then just mission them. I got my main party pets from 20 to 40 that way. and didn't raise a finger. And my 70 pets will be ready to level up a good bit when 71 and up is available.

Drill them in the third region one by one wiht 2 good pets (a tank and damage dealer, then put the level pet in the third slot for least cahnce of insta-death)

You can also put your pets on mission too PLUS sometimes if you are lucky you might get Experience Orbs from battle spoils or you can procure a few from the Trade Broker.
This is what I had to do too and sometimes I even managed to find a decent pet on the Advanced Search Page too.

Edited:
Oops..sorry, the mission thing was already mentioned...hooray for my awesome non-reading skills!!!

honestly the festival zone is one of the fastest way that i have found, you pop open an xp boost during a double xp weekend and just battle evrything in sight. Since that zone level up to your level you alwais have a good amount of xp at the end of a fight and potentialy finding rare themmed is alwais a plus. On the down side those zones are not alwais avalable but in that case there is alwais the beginning of the LG that can help as long as you have a good tank and equipement ^-^