Here we'll use a technique similar to one we used earlier to alter a layer mask. We'll create a path and then paint along that path to create a border.
Press Command-J (PC: Control-J) to duplicate the Background layer. Then use the Image>Canvas Size command, or press Command-Option-C (PC: Control-Alt-C), to add 1 inch of canvas (with the Relative checkbox turned on) to both the width and height. Click on the Create a New Layer icon at the bottom of the layers palette to add a new layer on top of the copied Background layer. This is where you'll add the border.
Press-and-hold the Command key (PC: Control key) and click on the thumbnail of the copied Background layer (Layer 1, in my example) to create a selection of your image. Then switch to the Paths palette (nested behind the Layers palette by default) and from the flyout menu, choose Make Work Path. In the resulting dialog, enter a Tolerance of 0.5 pixels.
Choose the Brush tool (B) and, in the Options Bar, pick a brush shape from the Brush Picker, then set the brush opacity. In this example, I used a 66-pixel brush called Dry Brush Tip Light Flow from the default set of brushes, but don't forget you can always tweak your brush in the Brushes palette. Click on the Foreground color swatch at the bottom of the Toolbox, and from the resulting Color Picker, choose the color you want to use. I used black in this case.
Make sure the blank layer is active and then switch back to the Paths palette. Press-and-hold the Option key (PC: Alt key) and click on the Stroke Path with Brush icon (second from the left at the bottom of the Paths palette). In the Stroke Path dialog, choose Brush from the Tool pop-up menu, if it is not already selected, and turn on the Simulate Pressure checkbox. Click OK and the brush will paint along the path (on the active layer).
In this example, I repeated Steps Three and Four, but this time used the Airbrush Dual Brush Soft Round 45 brush.