You'll have to do this manually. Create a new matte the color you want for the border. Put that under the PIP video, and scale it just a little bit larger than the PIP.
The "roughen edges" effect can be used to create a border. Play with the settings.
From an earlier post:
"One of the basic tasks that I do repeatedly is create frames for cropped, resized, or lower resolution video clips using the Title Maker. It is a simple sequence with two tracks, video on lower and frame above. To make the frame, I just put the cropped, resized video on track one, then open the title maker and draw a box over the video, being sure to match the size neatly. Next, I add a stroke to the box then un-check the Fill Color attribute toggle of the box. That leaves the stroke as a frame. Then I adjust the stroke's attributes until it looks the way I want and then lay the title\frame over the video on the timeline. Done. To repeat the effect on another clip of the same size\proportion, I just duplicate the sequence in the project widow, rename it, then replace the video track in the sequence while keeping the frame intact. Any motion attributes can be copied and pasted."
Lastly you use the sequence just like a video clip for other sequences.