It does depend, but I've found that many of them can be made to be region free or changed into a particular region. You just have to search the net exhaustively to get the codes.
Google the hell out of this as suggested by the second poster. In addition to his suggestion, I'd also suggest a Google search like "region+free+code", adding in the brand/model number. Several of the websites containing the codes are free, but more and more are coming back with a "small charge" for the info. Just keep looking and be a bit creative with your search, and you'll eventually come up with something.
It may take you time to find info about it. I've bought a "no name" portable DVD brand at Argos....took days to find the right codes, but eventually got it to work by finding the same brand, but different model number.
As an aside, I had a situation last year with a DVD recorder that had a worldwide multi-region fix freely available on the net. However, the fix simply did not work on my DVD machine, and I was literally minutes from returning the thing when I came across a slight modification just for units shipped into the ROI/UK. Worked like a charm.
Best of luck (and by the way, isn't it TOTALLY absurd to make a portable DVD player region specific?!?).