How to support freestanding trellis with 2x4 legs
I'm not sure if this will work for your exact situation, but you could use 2 or 4 "deck blocks" to anchor the trellis in place.



These are made to hold a 2x board in the cross or a 4x4 in the "socket".  You could connect your side legs of the trellis with a length of pressure treated 2x4 and place this block in the center.  Then use concrete screws to attach the 2x4 to the deck block.  The idea would be to bury the deck block so the 2x4 sets on the ground to stop it from rocking. 

If you think you needed it to be more stable, you could get a block for each corner and use galvanized brackets and concrete anchors to attach them to your feet.  Totally or partially bury them to level the trellis.

The advantage is that you get a pre-cast concrete footing without the need to manually mix and pour concrete and it's relatively easy to move if you ever needed to (easier than a typical post concreted into a hole in the ground).

But, that said, getting a single pressure treated 4x4, cutting it into 2' sections and concreteing those into the ground doesn't sound like a terrible option either.

I'd worry about stakes or something similar being pulled out by the wind.  With a free standing structure, the mass/stability of the footings is the only thing that can hold it in place.