Amused wrote:
I'm quite certain that I saw Tommy Silva (This Old House) use a specific
power tool to automatically cope the joints. And I'm relatively certain he
said it cost about $1500.

James...

One could also either install a "coping" foot on a jigsaw, or build one
of those triangular coping boxes. The box just might work with a
Rotozip. Personally, I do them by hand and finish up with a Dremel with
a carbide rasp. After 2 or 3, they go quickly.

Collins Coping foot:
http://www.garymkatz.com/Tool%20Reviews/CollinsCopingFoot.htm

By hand:

Slice the molding @ 45 degrees in the miter saw (like an inside miter
corner)
Darken the cut line with a pencil
Cut the cope near the line with a coping saw
Grind to the line with the Dremel, including the back bevel

Barry