Sadly, Nintendo made it so that virtual console games (stored as channels) can't be transferred from one Wii to another, since that would certainly put a hamper in their virtual console profits. As such, I'm relatively confident that there's no way to transfer those channels to your parents' new Wii. Sorry to say. =(
Of course, there's a small chance I might be wrong, so give Nintendo a call and ask 'em directly. You'll find their number at the bottom of the page, via the "Contact Us" link.