If the cruise line itself is offering airport to pier bus transportation, I would think that would be about the easiest way for your parents, except for needing to transport their own luggage for a while at HND.

I haven't seen any concrete evidence of a takkyubin serving cruise passengers departing from Osanbashi yet, but I'd be happy to be proven wrong. We're in much the same boat as your parents (no pun intended), though since posting to the other thread mentioned we have actually found a pair of fellow cruisers willing to share the cost of a large taxi from Shinjuku to the port.

It might be worthwhile to have your parents join the roll-call for their cruise on Cruise Critic dot com and see if a similar opportunity might present itself?