I don't think there are active tree frogs. Maybe the golden bell frogs which ebony stated? But I never even seen them upclose. From what I see they just hang around in a corner of the tank or on the ornaments. They're only active around feeding time, maybe misting? Also mating time (obv), And sometimes just exploring around at night. Frogs in general arent overly active, though I get what you mean. Like I have an american toad and she will sit in one spot, then move to another ten mins later or sometimes 40 mins later. But thats an exception. All I know is that the active frogs are:
FBT's
Dart frogs and mantellas
Clawed frogs(more of the xenopus laevis)
I know that some north american frogs -CAN- be active but mainly just lounge around.

As for tree frogs besides what ebony just stated, I dont know any other tree frog that is active(I was doing the same search myself a while ago).
But you know, there are individuals in each species. You may end up getting lucky and find the four leaf clover of the frog world and come across an active healthy specimen. Who knows. My guess is try:
-Cuban tree frogs(solitary frogs, but I seen em move more than the other tree frogs in the stores).
-Green Tree frog(Seen them SOMETIMES move around more than other tree frogs)

But if you want something hands down active, go for firebelly toads. They may not be tree frogs, but hey they're gorgeous, have an awesome coloring, they will use up all the space(Had em), and they're vocal calls is endearing. Or you could go for poison darts, but know that they are not that easy to keep up with, or so I keep getting told, but who knows.
As for activity in other frogs, like that other guy said depends on the season, temperature, moisture, and individual. SOmetimes even if they're really hungry.
Good luck.