Philips makes (or made) a small DVD player that stands up one end.
Maybe two inches thick. Can't remember the model name. Will post again
if I do.

Memorex made a similar player.

Spectra makes another DVD player that stands on end. However, it's a
"Hello Kitty" model, so I suspect your client could love or hate that
model! ;-)

The TEAC Reference series includes some narrow DVD players.

Yet another small DVD player, or really a computer with a DVD player:
The new $500 Apple Mac Mini computer. About 2" high and 6.5" inches
square. You'd need to add a keyboard, mouse, or remote control, but it
the Mac Mini can be mounted near a TV unobtrusively and connected to
the TV, if the TV has computer-style connections.

Somewhere, maybe on the web, I've seen a Mac Mini mounted to the back
of a big LCD or plasma TV screen.