Yes, there is in fact a veritable curnicopia of things you can do to help your pet gain Training Points. Take your pet outside a major city, and have him watch duels for a few hours. You can't go AFK, since you will have to acknowledge it, every time he gains another Training Point. Smarter than they look, these beasties.
Another way, would be to have him solo mobs. Don't even sting or Hunter's Mark the mobs, since he have to take the mob completely alone. After about two hours of this, if you have a high killspeed, your pet will gain a humongous chunk of Training points in one big wallop. Don't be discouraged if it takes a while, because sometimes you just have to keep doing it.
If you are lower than 40, you can head for Winterspring. This is something very very few people know about. If you can get there below 40, and go to the far south of Winterspring, you will find Demons. We don't know if it is a bug or not, but if you don't have a Hearthstone, your pet can actually tank those demons. As far as we know, it's the only mob type this works on. Killing those will net you enormous amounts of xp, and your pet will gain enough Training Points to become a little furball of Godlike Fury.
Or, you could... well, I don't know if I should say this. It is something that might not be for you. I mean, it takes a real Hunter to pull this off. Ah well, I am going to say it, but don't say I didn't warn you.
You can... if you have the mental faculty...
READ THE GOD DAMNED STICKY YOU LAZY *******! EVERY QUESTION ANSWERED HERE! SURPRISE SURPRISE! THAT MEANS YOUR QUESTION TOO!
Seriously, why can't people read the stickies when they got such horrifyingly basic questions?