As far as the old PSP goes, I have no idea.
I have a PSVita, so all I would have to do is find a torrent for the DLC, or the actual DLC itself, download it onto my computer, hook up the handheld to the PC and then transfer the files.
If you have a USB jack on your PSP, then you can do the same. Or you should be able to. If not, you need to open up the PSP, take out the wifi card and replace it with a new one. That's not something I would do, but then, I'm lazy and inexperienced with console modifications.