OK, a couple things can work. First off, try dropping “Bevel Alpha” on your clip. That will give a, well, bevelled edge to the PIP. If you want to put a colored border around the PIP, add Radial Shadow (it’s in Perspective, along with Bevel Alpha). You can change the color of the “shadow” to whatever color you like, and if you play with the projection distance and light source perameters, you can actually get a border around your PIP. Not super easy, but it will do what you want.
Otherwise, you could always create a border element in Photoshop or in the titler that’s just a little larger than your PIP element and put it on the timeline between the background layer and the PIP layer.
Hope one of these ideas helps!
– Dex