Well, I know how to do it in Photoshop....but haven't used Paintshop Pro, so I'm not sure if the directions are the same. I'll provide my instructions just in case they're useful and will poke through my bookmarks and see if I have any PSP tutorials listed.Does the image need to be transparent against a background color? (I.e. do you need to have the pixels next to the 1-pix area be semi transparent to that background color to avoid fringing?) That's the usual case, as opposed to being transparent against white.
What I usually do is create a new background layer filled with the color I want transparent. Then I expand my canvas by 1 pix in each direction (for the transparent area). Then I use "save for web" and select "transparency", and then select the color I want for the transparent color as the "matte" color.
Issues appear if you have that same color in your image and don't want them transparent...usually then I use a similar but not exactly the same color for my background, so the colors within the image don't turn out transparent.
If you don't have pixels that need to be semi-transparent with the background (i.e. no drop shadows, just hard edges) then you can pick any old color that's not in your image to be background color and be transparent. That's usually what is done for buttons or ads that will be used on multiple sites. But you have to make sure the colors in your edges are at 100% color or they'll be semi transparent to the background used in the graphics program, and that may cause weird "fringing" on certain backgrounds.
Hope that was helpful...I haven't had my coffee yet so it's a little rambling I'm afraid!