I have a need to get a wire to an alarm screen that is within a operable door. It's basically a door within a door. I haven't done one like this in a long time.
Sentrol (now GE) used to make a "coil cord" that you'd drill a 3/4" hole in both the door and jamb and had two wires within the coil, screw terminals at each end. They were very durable but I can't find them anywhere now.
Does anyone know of something that would work instead of having to expose a wire.
I do remember a "transfer hinge" that had the same idea. But then I can see issues with being a "different" look than the designer hinges or something.

What you want is an electrified hinge.

Talk to the vendor of the door hardware, you may be able to get the electrified hinge to match the other hinges.

Rocky Mountain Hardware will do this. 

Assuming you mean two conductors... you could always check the resistance across a hinge from one part to the other; oil it, work in the oil and see if it sill conducts; then if it works use one as positive and the other as negative. Not 120VAC, please!

I've used these before for getting power to electrified locksets:

[Link: speedwaymotors.com]

May not work for your application though because they break contact when the door is open.  If you only need continuity when the door is closed then I'd recommend them.

 

I have about a hundred of these installed with SDC lock sets and no issues.

[Link: sdcsecurity.com]

Were they a p.i.a. to install? Looks like the need to drill/ route or chisel.

Not too bad, but you do have to drill first using the template and then you press the contacts in the hole you drilled and trace around the flange and that needs to be chiseled out.

The contacts are spring loaded and are adjustable.  I tried them first at my own place where they've been installed and maintenance free on three doors for almost 10 years now.

[Link: grisk.com]

It's not a commercial job, high end residential.